diff --git a/.gitignore b/.gitignore
index ad486adcf29a1d95fd5c0ba08b3dbd9abc73ff2d..6f6cda65ece1cdca850f4f19f68d8e3d9ed63cf4 100644
--- a/.gitignore
+++ b/.gitignore
@@ -53,19 +53,23 @@
 *.svg
 *.fig
 *.md5
+*.xdmf
+*.h5
+*.dep
+*.csv 
 
 # Ignoriere Bilder und Graphiken sowie Videos und Musik
-#*.png
-#*.jpg
-#*.jpeg
-#*.eps
+*.png
+*.jpg
+*.jpeg
+*.eps
 *.svg
 *.pgf
-#*.gif
-#*.avi
-#*.mp4
-#*.mp3
-#*.xcf
+*.gif
+*.avi
+*.mp4
+*.mp3
+*.xcf
 
 # always consider files containing source code regardless of their name
 !*.cc
@@ -78,5 +82,7 @@
 
 # Directories
 demo/
+output/
+plots/
 FEniCS_Repository/
 __pycache__/
diff --git a/LDDsimulation/LDDsimulation.py b/LDDsimulation/LDDsimulation.py
index a9ddac2ccfe46c2c93851f5f8050a5ab11c27df2..9af6a2a580659deb5c6a82860824107d261a8b7e 100644
--- a/LDDsimulation/LDDsimulation.py
+++ b/LDDsimulation/LDDsimulation.py
@@ -355,6 +355,9 @@ class LDDsimulation(object):
         # r_cons.close()
         # energy.close()
         df.list_timings(df.TimingClear.keep, [df.TimingType.wall, df.TimingType.system])
+        with open(self.output_dir+"timings.txt", "w") as timefile:
+            timefile.write(df.timings)
+            
         df.dump_timings_to_xml(self.output_dir+"timings.xml",df.TimingClear.keep)
 
 
@@ -867,7 +870,7 @@ class LDDsimulation(object):
                                     the interface defined by the dolfin points in
                                     interface_def_points
         """
-        if not interface_def_points:
+        if interface_def_points is None:
             interface_def_points = self.interface_def_points
         else:
             # overwrite what has been set by init()
@@ -895,7 +898,6 @@ class LDDsimulation(object):
             # marker value gets internally set to global_index+1.
             # The reason is that we want to mark outer boundaries with the value 0.
             self.interface[num].mark(self.interface_marker, self.interface[num].marker_value)
-            # print("Global interface vertices:")
             self.interface[num].init_interface_values(self.interface_marker, self.interface[num].marker_value)
             # print(self.interface[num])
 
diff --git a/RR-multi-patch-plus-gravity/RR-multi-patch-with-gravity.py b/RR-multi-patch-plus-gravity/RR-multi-patch-with-gravity.py
index 7916f0ff1549303f235ac06780b1af06c2b5694c..d1375f3936e370f9348313538e1558d60131f66f 100755
--- a/RR-multi-patch-plus-gravity/RR-multi-patch-with-gravity.py
+++ b/RR-multi-patch-plus-gravity/RR-multi-patch-with-gravity.py
@@ -9,6 +9,24 @@ import LDDsimulation as ldd
 import functools as ft
 # import ufl as ufl
 
+# init sympy session
+sym.init_printing()
+
+# ----------------------------------------------------------------------------#
+# ------------------- MESH ---------------------------------------------------#
+# ----------------------------------------------------------------------------#
+mesh_resolution = 30
+# ----------------------------------------:-------------------------------------#
+# ------------------- TIME ---------------------------------------------------#
+# ----------------------------------------------------------------------------#
+timestep_size = 0.01
+number_of_timesteps = 500
+# decide how many timesteps you want analysed. Analysed means, that we write
+# out subsequent errors of the L-iteration within the timestep.
+number_of_timesteps_to_analyse = 11
+starttime = 0
+
+
 # ----------------------------------------------------------------------------#
 # ------------------- Domain and Interface -----------------------------------#
 # ----------------------------------------------------------------------------#
@@ -117,19 +135,6 @@ isRichards = {
     4: True
     }
 
-# ----------------------------------------------------------------------------#
-# ------------------- MESH ---------------------------------------------------#
-# ----------------------------------------------------------------------------#
-mesh_resolution = 20
-# ----------------------------------------:-------------------------------------#
-# ------------------- TIME ---------------------------------------------------#
-# ----------------------------------------------------------------------------#
-timestep_size = 0.01
-number_of_timesteps = 500
-# decide how many timesteps you want analysed. Analysed means, that we write
-# out subsequent errors of the L-iteration within the timestep.
-number_of_timesteps_to_analyse = 11
-starttime = 0
 
 # Dict of the form: { subdom_num : viscosity }
 viscosity = {
@@ -164,12 +169,13 @@ L = {
     4: {'wetting': 0.25}
 }
 
+lamdal_w = 23
 # subdom_num : lambda parameter for the L-scheme
 lambda_param = {
-    1: {'wetting': 15},
-    2: {'wetting': 15},
-    3: {'wetting': 15},
-    4: {'wetting': 15}
+    1: {'wetting': lamdal_w},
+    2: {'wetting': lamdal_w},
+    3: {'wetting': lamdal_w},
+    4: {'wetting': lamdal_w}
 }
 
 
diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/domain_marker.pvd b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/domain_marker.pvd
deleted file mode 100644
index 11d1c43fb192052f82ab6693f1e8d3e4992fc6fd..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/domain_marker.pvd
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0"?>
-<VTKFile type="Collection" version="0.1">
-  <Collection>
-    <DataSet timestep="0" part="0" file="domain_marker000000.vtu" />
-  </Collection>
-</VTKFile>
diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/domain_marker000000.vtu b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/domain_marker000000.vtu
deleted file mode 100644
index 2f2bd79e4bd853594e2dc90ee1a2f77583d4e25d..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/domain_marker000000.vtu
+++ /dev/null
@@ -1,18 +0,0 @@
-<?xml version="1.0"?>
-<VTKFile type="UnstructuredGrid"  version="0.1"  >
-<UnstructuredGrid>
-<Piece  NumberOfPoints="839" NumberOfCells="1548">
-<Points>
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/global_mesh.pvd b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/global_mesh.pvd
deleted file mode 100644
index 6dd2a80f0b24ed425f6a3b676528d78d3ba066b4..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/global_mesh.pvd
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/global_mesh000000.vtu b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/global_mesh000000.vtu
deleted file mode 100644
index ea4225d108b7c5f68092c300e1f4fd7b20da6513..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/global_mesh000000.vtu
+++ /dev/null
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/interface_marker_global.pvd b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/interface_marker_global.pvd
deleted file mode 100644
index 24d98b972deb99878ae5b3127bd0a84416b60d42..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/interface_marker_global.pvd
+++ /dev/null
@@ -1,6 +0,0 @@
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/interface_marker_global000000.vtu b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/interface_marker_global000000.vtu
deleted file mode 100644
index e8b5765fe5c7d7616081eb2d05f64ad7a9780860..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/interface_marker_global000000.vtu
+++ /dev/null
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deleted file mode 100644
index 5bc1ac8f8ea043e069babdc0353521759ce8ec87..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv
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Binary files a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25_solution.h5 and /dev/null differ
diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25_solution.xdmf b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25_solution.xdmf
deleted file mode 100644
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--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25_solution.xdmf
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.h5 b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.h5
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Binary files a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.h5 and /dev/null differ
diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf
deleted file mode 100644
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--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv
deleted file mode 100644
index ef105d399722b5c0574da3aeb41c798784c956d7..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv
+++ /dev/null
@@ -1,117 +0,0 @@
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv
deleted file mode 100644
index e3a0035ceb8a28a54de51402019903a32e78bb2a..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv
+++ /dev/null
@@ -1,7 +0,0 @@
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.h5 b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.h5
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.xdmf b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.xdmf
deleted file mode 100644
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--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.xdmf
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv
deleted file mode 100644
index 244fe0385c67162cfcc2f6bd0635e5126ff7ad20..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv
+++ /dev/null
@@ -1,117 +0,0 @@
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv
deleted file mode 100644
index ac8a5cc576a7228b24d6aa38a3d6b5e523ce7948..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv
+++ /dev/null
@@ -1,7 +0,0 @@
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.h5 b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.h5
deleted file mode 100644
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Binary files a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.h5 and /dev/null differ
diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.xdmf b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.xdmf
deleted file mode 100644
index b7efbe553eaccd62947f1243e1e32cfe9f2f4d1f..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.xdmf
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf
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index 0583464ee461c12f4ad2cde7b13403a432de8440..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf
+++ /dev/null
@@ -1,2114 +0,0 @@
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv
deleted file mode 100644
index 35b37fca50b2575a6a9fffbe6de68b89f400878f..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv
+++ /dev/null
@@ -1,117 +0,0 @@
-iteration	wetting
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-21	0.000206926064136017
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv
deleted file mode 100644
index c917d9ec5f73a839cfd907a97f5930e4136e5265..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv
+++ /dev/null
@@ -1,7 +0,0 @@
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.h5 b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.h5
deleted file mode 100644
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Binary files a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.h5 and /dev/null differ
diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.xdmf b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.xdmf
deleted file mode 100644
index 0b746f8340faa1d557c9c53172019037916dab34..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_solution.xdmf
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.h5 b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.h5
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Binary files a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.h5 and /dev/null differ
diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf
deleted file mode 100644
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--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25solution_iterations_at_t0.00.xdmf
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diff --git a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv b/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv
deleted file mode 100644
index 0f546dde8e28a29b10421cf00b7ede2a982e2566..0000000000000000000000000000000000000000
--- a/RR-multi-patch-plus-gravity/output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time0.0000.csv
+++ /dev/null
@@ -1,117 +0,0 @@
-iteration	wetting
-2	0.0017627188941890316
-3	0.006051966404871039
-4	0.0018531677429427253
-5	0.002468510463764524
-6	0.001972524748447661
-7	0.0012291783507406334
-8	0.0017894919394043445
-9	0.0009002286327284067
-10	0.00114307907735503
-11	0.0009535116776464829
-12	0.0007095248690185984
-13	0.0008569244304545334
-14	0.00043664512388305094
-15	0.0006644892347666877
-16	0.00043811119599686466
-17	0.0003979629663108126
-18	0.00044862962821393007
-19	0.00022899023751546597
-20	0.0003570754625776726
-21	0.00020178192960157378
-22	0.00024327911787865272
-23	0.0002142475586018207
-24	0.0001284427065576706
-25	0.0001952259857338133
-26	9.264100682061754e-05
-27	0.00013707778326825225
-28	0.00010431175517936185
-29	8.124849140657581e-05
-30	9.966865697350039e-05
-31	4.6706346759637744e-05
-32	7.971998695005236e-05
-33	4.824152877237164e-05
-34	4.848522654164521e-05
-35	5.20244590932665e-05
-36	2.7353247248075956e-05
-37	4.302984382756298e-05
-38	2.3274723299410523e-05
-39	2.9975485984235653e-05
-40	2.5367139368289234e-05
-41	1.615111751202211e-05
-42	2.3772907686609982e-05
-43	1.1262462527842849e-05
-44	1.7009748883749463e-05
-45	1.2607022599242518e-05
-46	1.0362694578906172e-05
-47	1.2136822259785492e-05
-48	5.88658257055977e-06
-49	9.919237425701391e-06
-50	5.8627032944655235e-06
-51	6.096038546783087e-06
-52	6.351683072579284e-06
-53	3.4808845626769865e-06
-54	5.310478195784179e-06
-55	2.8291980332805254e-06
-56	3.764915650691256e-06
-57	3.055298865714045e-06
-58	2.046038757008633e-06
-59	2.932935505461565e-06
-60	1.3851895112915048e-06
-61	2.104896615492081e-06
-62	1.5195198051094468e-06
-63	1.3203167217685683e-06
-64	1.481512452802188e-06
-65	7.298224705460172e-07
-66	1.2294239000555032e-06
-67	7.019965124088058e-07
-68	7.678533397805249e-07
-69	7.778890997492493e-07
-70	4.4188185716905496e-07
-71	6.498480910250319e-07
-72	3.4175063646531107e-07
-73	4.763854669138986e-07
-74	3.701895544615557e-07
-75	2.5830104791375587e-07
-76	3.5963730871316223e-07
-77	1.720068376269117e-07
-78	2.625384639514598e-07
-79	1.8570523373285156e-07
-80	1.6745859402494965e-07
-81	1.793013954800104e-07
-82	9.173487783762524e-08
-83	1.544333164646315e-07
-84	8.505414540762688e-08
-85	9.584410918437127e-08
-86	9.405874228055302e-08
-87	5.783871347107623e-08
-88	8.001020422148802e-08
-89	4.236907554639028e-08
-90	5.929133759638785e-08
-91	4.423753833475914e-08
-92	3.331702355987764e-08
-93	4.447928381656317e-08
-94	2.185793641337586e-08
-95	3.224740068222563e-08
-96	2.189162454875031e-08
-97	2.1945393907250182e-08
-98	2.1288073610707243e-08
-99	1.1944478476405406e-08
-100	1.8401595375625745e-08
-101	1.0094002937007808e-08
-102	1.1494404131046821e-08
-103	1.0775817515354623e-08
-104	7.470204541044261e-09
-105	8.764879821078707e-09
-106	4.775332153318827e-09
-107	6.773692965228832e-09
-108	4.279173942175915e-09
-109	3.726696944303678e-09
-110	3.892825043859314e-09
-111	2.495367141441267e-09
-112	2.4891266286614854e-09
-113	1.6773708555683332e-09
-114	1.565271978684441e-09
-115	1.2220298107760972e-09
-116	7.325608003554354e-10
-117	8.508642833342012e-10
diff --git a/RR-multi-patch-plus-gravity/plots/Tikzcache/Errornorm-exact-solution-over-time-with-gravity.dep b/RR-multi-patch-plus-gravity/plots/Tikzcache/Errornorm-exact-solution-over-time-with-gravity.dep
index 8c01c28cd37ab38ec50a57ebc9a8cd0ba6609515..1bca4db5c72d7f3f255efb80ab9b52918f0f2dc8 100644
--- a/RR-multi-patch-plus-gravity/plots/Tikzcache/Errornorm-exact-solution-over-time-with-gravity.dep
+++ b/RR-multi-patch-plus-gravity/plots/Tikzcache/Errornorm-exact-solution-over-time-with-gravity.dep
@@ -1,2 +1,4 @@
-Tikzcache/Errornorm-exact-solution-over-time-with-gravity.pdf: ../output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv
-Tikzcache/Errornorm-exact-solution-over-time-with-gravity.pdf: ../output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv
+Tikzcache/Errornorm-exact-solution-over-time-with-gravity.pdf: ../output/mesh_res30_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.075_gravitiy_True_lambda23_Lw0.25_L2_errornorms_over_time.csv
+Tikzcache/Errornorm-exact-solution-over-time-with-gravity.pdf: ../output/mesh_res30_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.075_gravitiy_True_lambda23_Lw0.25_L2_errornorms_over_time.csv
+Tikzcache/Errornorm-exact-solution-over-time-with-gravity.pdf: ../output/mesh_res30_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.075_gravitiy_True_lambda23_Lw0.25_L2_errornorms_over_time.csv
+Tikzcache/Errornorm-exact-solution-over-time-with-gravity.pdf: ../output/mesh_res30_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.075_gravitiy_True_lambda23_Lw0.25_L2_errornorms_over_time.csv
diff --git a/RR-multi-patch-plus-gravity/plots/Tikzcache/Errornorm-exact-solution-over-time-with-gravity.png b/RR-multi-patch-plus-gravity/plots/Tikzcache/Errornorm-exact-solution-over-time-with-gravity.png
index 95c93a57929390ac487cacb4abe365c21350149e..a71337e67b9d560b75a7fd522da9c48a3d9f7204 100644
Binary files a/RR-multi-patch-plus-gravity/plots/Tikzcache/Errornorm-exact-solution-over-time-with-gravity.png and b/RR-multi-patch-plus-gravity/plots/Tikzcache/Errornorm-exact-solution-over-time-with-gravity.png differ
diff --git a/RR-multi-patch-plus-gravity/plots/meshres20_dt0.01_exact_solution_error_norms.tex b/RR-multi-patch-plus-gravity/plots/meshres20_dt0.01_exact_solution_error_norms.tex
index 67b04f4d24b470a032c9e04d9562e6bfcfab43d9..5a4307fa096f3c96763e1991d691f69f71243339 100644
--- a/RR-multi-patch-plus-gravity/plots/meshres20_dt0.01_exact_solution_error_norms.tex
+++ b/RR-multi-patch-plus-gravity/plots/meshres20_dt0.01_exact_solution_error_norms.tex
@@ -17,11 +17,11 @@
 % %     \path[draw,dashed,thick] (3.13,0) -- (3.13,5.2);
         \begin{axis}[%
             width=\textwidth,
-            title={ $\frac{\|p_{w,l}^n - p_{w,l}^{n,h}\|_{L^2}}{\|p_{w,l}^n\|_{L^2}}$  over time $t$,  $ h \approx 0.112$, $\tau = 1\cdot 10^{-2}$ },
+            title={ $\frac{\|p_{w,l}^n - p_{w,l}^{n,h}\|_{L^2}}{\|p_{w,l}^n\|_{L^2}}$  over time $t$,  $ h \approx 0.113$, $\tau = 1\cdot 10^{-2}$ },
         % 	    axis lines=left,
         % 	legend style = {draw=none},
             legend cell align = left,
-            xlabel= {timesteps},
+            xlabel= {time},
             ylabel= {$\frac{\|p_{w,l}^n - p_{w,l}^{n,h}\|_{L^2}}{\|p_{w,l}^n\|_{L^2}}$},
             xmin= 0,
 %             xmax= 53,
@@ -30,20 +30,22 @@
         	grid= both, %major or minor
             axis line style={-Latex[round]},
             legend style={
-%                 anchor=north east,
-%                 at={(1,1)},
+                anchor=south east,
+                at={(1,0)},
 %                 font=\tiny
                 inner sep=1ex,
 %                 /tikz/every even column/.append style={column sep=0.5cm}
                 row sep=.5ex,
             },
             legend entries={$\frac{\|p_{w,1}^n - p_{w,1}^{n,h}\|_2}{\|p_{w,1}^n\|_2} \text{ on } \dom_1$,
-                            $\frac{\|p_{w,2}^n - p_{w,2}^{n,h}\|_2}{\|p_{w,2}^n\|_2} \text{ on } \dom_2$},
+                            $\frac{\|p_{w,2}^n - p_{w,2}^{n,h}\|_2}{\|p_{w,2}^n\|_2} \text{ on } \dom_2$,
+                            $\frac{\|p_{w,3}^n - p_{w,3}^{n,h}\|_2}{\|p_{w,3}^n\|_2} \text{ on } \dom_3$,
+                            $\frac{\|p_{w,4}^n - p_{w,4}^{n,h}\|_2}{\|p_{w,4}^n\|_2} \text{ on } \dom_4$},
             ] % end of axis options %col sep=comma,
-            \addplot table [x=timestep, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv};%
-            \addplot table [x=timestep, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25_L2_errornorms_over_time.csv};%
-% %             \addplot table [col sep=comma] {../output/subdomain1_subsequent_iteration_error_for_phase_wetting_at_time0.csv};%
-% % %             \addplot table [col sep=comma] {../output/subdomain2_subsequent_iteration_error_for_phase_wetting_at_time0.csv};%        
+            \addplot table [x=time, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda17_Lw0.25_L2_errornorms_over_time.csv};%
+            \addplot table [x=time, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda17_Lw0.25_L2_errornorms_over_time.csv};%
+            \addplot table [x=time, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda17_Lw0.25_L2_errornorms_over_time.csv};%
+            \addplot table [x=time, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda17_Lw0.25_L2_errornorms_over_time.csv};%
         \end{axis}
     \end{tikzpicture}  
 
diff --git a/RR-multi-patch-plus-gravity/plots/meshres20_dt0.01_subsequent_errors.tex b/RR-multi-patch-plus-gravity/plots/meshres20_dt0.01_subsequent_errors.tex
index c6b94230101116e73362898c583903f76635ef12..423d17752d58a72a42045981b8d8f3ba48ff4457 100644
--- a/RR-multi-patch-plus-gravity/plots/meshres20_dt0.01_subsequent_errors.tex
+++ b/RR-multi-patch-plus-gravity/plots/meshres20_dt0.01_subsequent_errors.tex
@@ -10,7 +10,7 @@
 \usepackage{pgfplotstable}
 
 \begin{document}
-    \foreach \timestep in {0.00,0.04,0.08,0.12,0.16,0.20,0.24,0.28,0.32,0.36}{
+    \foreach \timestep in {0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,4.5}{
         % Generation of Subsequent_errors_t0.00
         \tikzsetnextfilename{RR-2-patch-subsequent_errors_t\timestep}
     \tikzset{external/force remake}
@@ -18,7 +18,7 @@
 % %     \path[draw,dashed,thick] (3.13,0) -- (3.13,5.2);
         \begin{semilogyaxis}[%
             width=\textwidth,
-            title={ Subsequent errors for $t = 0$,  $ h \approx 0.112$, $\tau = 4\cdot 10^{-4}$ },
+            title={ Subsequent errors for $t = 0$,  $ h \approx 0.113$, $\tau =1\cdot 10^{-2}$ },
         % 	    axis lines=left,
         % 	legend style = {draw=none},
             legend cell align = left,
@@ -35,13 +35,15 @@
 %                 at={(1,1)},
                 font=\tiny
             },
-            legend entries={$\bigl\|p_l^i - p_l^{i-1}\bigr\|_{L^2(\dom_1)}$,
-                            $\bigl\|p_l^i - p_l^{i-1}\bigr\|_{L^2(\dom_2)}$},
+            legend entries={$\bigl\|p_1^i - p_1^{i-1}\bigr\|_{L^2(\dom_1)}$,
+                            $\bigl\|p_2^i - p_2^{i-1}\bigr\|_{L^2(\dom_2)}$,
+                            $\bigl\|p_3^i - p_3^{i-1}\bigr\|_{L^2(\dom_3)}$,
+                            $\bigl\|p_4^i - p_4^{i-1}\bigr\|_{L^2(\dom_4)}$},
             ] % end of axis options %col sep=comma,
-            \addplot table [x=iteration, y=wetting] {../output/mesh_res10_dt0.0004/subdomain1_dt0.0004_hmax0.112_lambda40_Lw0.25subsequent_iteration_errors_at_time\timestep.csv};%
-            \addplot table [x=iteration, y=wetting] {../output/mesh_res10_dt0.0004/subdomain2_dt0.0004_hmax0.110_lambda40_Lw0.25subsequent_iteration_errors_at_time\timestep.csv};%
-%             \addplot table [col sep=comma] {../output/subdomain1_subsequent_iteration_error_for_phase_wetting_at_time0.csv};%
-% %             \addplot table [col sep=comma] {../output/subdomain2_subsequent_iteration_error_for_phase_wetting_at_time0.csv};%        
+            \addplot table [x=iteration, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain1_dt0.01_hmax0.112_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time\timestep000.csv};%
+            \addplot table [x=iteration, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain2_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time\timestep000.csv};%
+            \addplot table [x=iteration, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain3_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time\timestep000.csv};%%        
+            \addplot table [x=iteration, y=wetting] {../output/mesh_res20_dt0.01_with_gravity/subdomain4_dt0.01_hmax0.113_gravitiy_True_lambda15_Lw0.25subsequent_iteration_errors_at_time\timestep000.csv};%
         \end{semilogyaxis}
     \end{tikzpicture}  
     }
diff --git a/TP-TP-layered-soil-case/TP-TP-layered_soil.py b/TP-TP-layered-soil-case/TP-TP-layered_soil.py
new file mode 100755
index 0000000000000000000000000000000000000000..7ecf9a728e057af3f5a92fd17fd9be9da67b59b6
--- /dev/null
+++ b/TP-TP-layered-soil-case/TP-TP-layered_soil.py
@@ -0,0 +1,546 @@
+#!/usr/bin/python3
+"""This program sets up a domain together with a decomposition into subdomains
+modelling layered soil. This is used for our LDD article with tp-tp and tp-r
+coupling.
+
+Along with the subdomains and the mesh domain markers are set upself.
+The resulting mesh is saved into files for later use.
+"""
+
+#!/usr/bin/python3
+import dolfin as df
+import mshr
+import numpy as np
+import sympy as sym
+import typing as tp
+import functools as ft
+import domainPatch as dp
+import LDDsimulation as ldd
+
+# init sympy session
+sym.init_printing()
+
+# ----------------------------------------------------------------------------#
+# ------------------- MESH ---------------------------------------------------#
+# ----------------------------------------------------------------------------#
+mesh_resolution = 4
+# ----------------------------------------:-------------------------------------#
+# ------------------- TIME ---------------------------------------------------#
+# ----------------------------------------------------------------------------#
+timestep_size = 0.005
+number_of_timesteps = 30
+# decide how many timesteps you want analysed. Analysed means, that we write
+# out subsequent errors of the L-iteration within the timestep.
+number_of_timesteps_to_analyse = 11
+starttime = 0
+
+l_param_w = 40
+l_param_nw = l_param_w
+
+# global domain
+subdomain0_vertices = [df.Point(0.0,0.0), #
+                        df.Point(13.0,0.0),#
+                        df.Point(13.0,8.0),#
+                        df.Point(0.0,8.0)]
+
+interface12_vertices = [df.Point(0.0, 7.0),
+                        df.Point(9.0, 7.0),
+                        df.Point(10.5, 7.5),
+                        df.Point(12.0, 7.0),
+                        df.Point(13.0, 6.5)]
+# subdomain1.
+subdomain1_vertices = [interface12_vertices[0],
+                        interface12_vertices[1],
+                        interface12_vertices[2],
+                        interface12_vertices[3],
+                        interface12_vertices[4], # southern boundary, 12 interface
+                        subdomain0_vertices[2], # eastern boundary, outer boundary
+                        subdomain0_vertices[3]] # northern boundary, outer on_boundary
+
+# vertex coordinates of the outer boundaries. If it can not be specified as a
+# polygon, use an entry per boundary polygon. This information is used for defining
+# the Dirichlet boundary conditions. If a domain is completely internal, the
+# dictionary entry should be 0: None
+subdomain1_outer_boundary_verts = {
+    0: [interface12_vertices[4], #
+        subdomain0_vertices[2], # eastern boundary, outer boundary
+        subdomain0_vertices[3],
+        interface12_vertices[0]]
+}
+
+
+# interface23
+interface23_vertices = [df.Point(0.0, 5.0),
+                        df.Point(3.0, 5.0),
+                        # df.Point(6.5, 4.5),
+                        df.Point(6.5, 5.0),
+                        df.Point(9.5, 5.0),
+                        # df.Point(11.5, 3.5),
+                        # df.Point(13.0, 3)
+                        df.Point(11.5, 5.0),
+                        df.Point(13.0, 5.0)
+                        ]
+
+#subdomain1
+subdomain2_vertices = [interface23_vertices[0],
+                        interface23_vertices[1],
+                        interface23_vertices[2],
+                        interface23_vertices[3],
+                        interface23_vertices[4],
+                        interface23_vertices[5], # southern boundary, 23 interface
+                        subdomain1_vertices[4], # eastern boundary, outer boundary
+                        subdomain1_vertices[3],
+                        subdomain1_vertices[2],
+                        subdomain1_vertices[1],
+                        subdomain1_vertices[0] ] # northern boundary, 12 interface
+
+subdomain2_outer_boundary_verts = {
+    0: [interface23_vertices[5],
+        subdomain1_vertices[4]],
+    1: [subdomain1_vertices[0],
+        interface23_vertices[0]]
+}
+
+
+# interface34
+interface34_vertices = [df.Point(0.0, 2.0),
+                        df.Point(4.0, 2.0),
+                        df.Point(9.0, 2.5),
+                        df.Point(10.5, 2.0),
+                        df.Point(13.0, 1.5)]
+
+# subdomain3
+subdomain3_vertices = [interface34_vertices[0],
+                        interface34_vertices[1],
+                        interface34_vertices[2],
+                        interface34_vertices[3],
+                        interface34_vertices[4], # southern boundary, 34 interface
+                        subdomain2_vertices[5], # eastern boundary, outer boundary
+                        subdomain2_vertices[4],
+                        subdomain2_vertices[3],
+                        subdomain2_vertices[2],
+                        subdomain2_vertices[1],
+                        subdomain2_vertices[0] ] # northern boundary, 23 interface
+
+subdomain3_outer_boundary_verts = {
+    0: [interface34_vertices[4],
+        subdomain2_vertices[5]],
+    1: [subdomain2_vertices[0],
+        interface34_vertices[0]]
+}
+
+# subdomain4
+subdomain4_vertices = [subdomain0_vertices[0],
+                        subdomain0_vertices[1], # southern boundary, outer boundary
+                        subdomain3_vertices[4],# eastern boundary, outer boundary
+                        subdomain3_vertices[3],
+                        subdomain3_vertices[2],
+                        subdomain3_vertices[1],
+                        subdomain3_vertices[0] ] # northern boundary, 34 interface
+
+subdomain4_outer_boundary_verts = {
+    0: [subdomain4_vertices[6],
+        subdomain4_vertices[0],
+        subdomain4_vertices[1],
+        subdomain4_vertices[2]]
+}
+
+
+subdomain_def_points = [subdomain0_vertices,#
+                      subdomain1_vertices,#
+                      subdomain2_vertices,#
+                      subdomain3_vertices,#
+                      subdomain4_vertices
+                      ]
+
+
+# interface_vertices introduces a global numbering of interfaces.
+interface_def_points = [interface12_vertices, interface23_vertices, interface34_vertices]
+adjacent_subdomains = [[1,2], [2,3], [3,4]]
+
+# if a subdomain has no outer boundary write None instead, i.e.
+# i: None
+# if i is the index of the inner subdomain.
+outer_boundary_def_points = {
+    # subdomain number
+    1: subdomain1_outer_boundary_verts,
+    2: subdomain2_outer_boundary_verts,
+    3: subdomain3_outer_boundary_verts,
+    4: subdomain4_outer_boundary_verts
+}
+
+isRichards = {
+    1: False,
+    2: False,
+    3: False,
+    4: False
+    }
+
+# Dict of the form: { subdom_num : viscosity }
+viscosity = {
+    1: {'wetting' :1,
+         'nonwetting': 1/50},
+    2: {'wetting' :1,
+         'nonwetting': 1/50},
+    3: {'wetting' :1,
+         'nonwetting': 1/50},
+    4: {'wetting' :1,
+         'nonwetting': 1/50},
+}
+
+# Dict of the form: { subdom_num : density }
+densities = {
+    1: {'wetting': 997,
+         'nonwetting': 1.225},
+    2: {'wetting': 997,
+         'nonwetting': 1.225},
+    3: {'wetting': 997,
+         'nonwetting': 1.225},
+    4: {'wetting': 997,
+         'nonwetting': 1.225}
+}
+
+gravity_acceleration = 9.81
+# porosities taken from
+# https://www.geotechdata.info/parameter/soil-porosity.html
+# Dict of the form: { subdom_num : porosity }
+porosity = {
+    1: 0.2,  # Clayey gravels, clayey sandy gravels
+    2: 0.22, # Silty gravels, silty sandy gravels
+    3: 0.37, # Clayey sands
+    4: 0.2 # Silty or sandy clay
+}
+
+# subdom_num : subdomain L for L-scheme
+L = {
+    1: {'wetting' :0.25,
+         'nonwetting': 0.25},
+    2: {'wetting' :0.25,
+         'nonwetting': 0.25},
+    3: {'wetting' :0.25,
+         'nonwetting': 0.25},
+    4: {'wetting' :0.25,
+         'nonwetting': 0.25}
+}
+
+# subdom_num : lambda parameter for the L-scheme
+lambda_param = {
+    1: {'wetting': l_param_w,
+         'nonwetting': l_param_nw},#
+    2: {'wetting': l_param_w,
+         'nonwetting': l_param_nw},#
+    3: {'wetting': l_param_w,
+         'nonwetting': l_param_nw},#
+    4: {'wetting': l_param_w,
+         'nonwetting': l_param_nw},#
+}
+
+
+## relative permeabilty functions on subdomain 1
+def rel_perm1w(s):
+    # relative permeabilty wetting on subdomain1
+    return s**2
+
+
+def rel_perm1nw(s):
+    # relative permeabilty nonwetting on subdomain1
+    return (1-s)**2
+
+
+## relative permeabilty functions on subdomain 2
+def rel_perm2w(s):
+    # relative permeabilty wetting on subdomain2
+    return s**3
+
+
+def rel_perm2nw(s):
+    # relative permeabilty nonwetting on subdosym.cos(0.8*t - (0.8*x + 1/7*y))main2
+    return (1-s)**2
+
+
+_rel_perm1w = ft.partial(rel_perm1w)
+_rel_perm1nw = ft.partial(rel_perm1nw)
+_rel_perm2w = ft.partial(rel_perm2w)
+_rel_perm2nw = ft.partial(rel_perm2nw)
+
+subdomain1_rel_perm = {
+    'wetting': _rel_perm1w,#
+    'nonwetting': _rel_perm1nw
+}
+
+subdomain2_rel_perm = {
+    'wetting': _rel_perm2w,#
+    'nonwetting': _rel_perm2nw
+}
+
+# _rel_perm3 = ft.partial(rel_perm2)
+# subdomain3_rel_perm = subdomain2_rel_perm.copy()
+#
+# _rel_perm4 = ft.partial(rel_perm1)
+# subdomain4_rel_perm = subdomain1_rel_perm.copy()
+
+# dictionary of relative permeabilties on all domains.
+relative_permeability = {
+    1: subdomain1_rel_perm,
+    2: subdomain1_rel_perm,
+    3: subdomain2_rel_perm,
+    4: subdomain2_rel_perm
+}
+
+# definition of the derivatives of the relative permeabilities
+# relative permeabilty functions on subdomain 1
+def rel_perm1w_prime(s):
+    # relative permeabilty on subdomain1
+    return 2*s
+
+def rel_perm1nw_prime(s):
+    # relative permeabilty on subdomain1
+    return 2*(1-s)
+
+# definition of the derivatives of the relative permeabilities
+# relative permeabilty functions on subdomain 1
+def rel_perm2w_prime(s):
+    # relative permeabilty on subdomain1
+    return 3*s**2
+
+def rel_perm2nw_prime(s):
+    # relative permeabilty on subdomain1
+    return 2*(1-s)
+
+_rel_perm1w_prime = ft.partial(rel_perm1w_prime)
+_rel_perm1nw_prime = ft.partial(rel_perm1nw_prime)
+_rel_perm2w_prime = ft.partial(rel_perm2w_prime)
+_rel_perm2nw_prime = ft.partial(rel_perm2nw_prime)
+
+subdomain1_rel_perm_prime = {
+    'wetting': _rel_perm1w_prime,
+    'nonwetting': _rel_perm1nw_prime
+}
+
+
+subdomain2_rel_perm_prime = {
+    'wetting': _rel_perm2w_prime,
+    'nonwetting': _rel_perm2nw_prime
+}
+
+# dictionary of relative permeabilties on all domains.
+ka_prime = {
+    1: subdomain1_rel_perm_prime,
+    2: subdomain1_rel_perm_prime,
+    3: subdomain2_rel_perm_prime,
+    4: subdomain2_rel_perm_prime
+}
+
+
+
+# S-pc-relation ship. We use the van Genuchten approach, i.e. pc = 1/alpha*(S^{-1/m} -1)^1/n, where
+# we set alpha = 0, assume m = 1-1/n (see Helmig) and assume that residual saturation is Sw
+# this function needs to be monotonically decreasing in the capillary pressure pc.
+# since in the richards case pc=-pw, this becomes as a function of pw a mono
+# tonically INCREASING function like in our Richards-Richards paper. However
+# since we unify the treatment in the code for Richards and two-phase, we need
+# the same requierment
+# for both cases, two-phase and Richards.
+def saturation(pc, n_index, alpha):
+    # inverse capillary pressure-saturation-relationship
+    return df.conditional(pc > 0, 1/((1 + (alpha*pc)**n_index)**((n_index - 1)/n_index)), 1)
+
+# S-pc-relation ship. We use the van Genuchten approach, i.e. pc = 1/alpha*(S^{-1/m} -1)^1/n, where
+# we set alpha = 0, assume m = 1-1/n (see Helmig) and assume that residual saturation is Sw
+def saturation_sym(pc, n_index, alpha):
+    # inverse capillary pressure-saturation-relationship
+    #df.conditional(pc > 0,
+    return 1/((1 + (alpha*pc)**n_index)**((n_index - 1)/n_index))
+
+
+# derivative of S-pc relationship with respect to pc. This is needed for the
+# construction of a analytic solution.
+def saturation_sym_prime(pc, n_index, alpha):
+    # inverse capillary pressure-saturation-relationship
+    return -(alpha*(n_index - 1)*(alpha*pc)**(n_index - 1)) / ( (1 + (alpha*pc)**n_index)**((2*n_index - 1)/n_index) )
+
+
+# note that the conditional definition of S-pc in the nonsymbolic part will be
+# incorporated in the construction of the exact solution below.
+S_pc_sym = {
+    1: ft.partial(saturation_sym, n_index=3, alpha=0.001),
+    2: ft.partial(saturation_sym, n_index=3, alpha=0.001),
+    3: ft.partial(saturation_sym, n_index=6, alpha=0.001),
+    4: ft.partial(saturation_sym, n_index=6, alpha=0.001)
+}
+
+S_pc_sym_prime = {
+    1: ft.partial(saturation_sym_prime, n_index=3, alpha=0.001),
+    2: ft.partial(saturation_sym_prime, n_index=3, alpha=0.001),
+    3: ft.partial(saturation_sym_prime, n_index=6, alpha=0.001),
+    4: ft.partial(saturation_sym_prime, n_index=6, alpha=0.001)
+}
+
+sat_pressure_relationship = {
+    1: ft.partial(saturation, n_index=3, alpha=0.001),
+    2: ft.partial(saturation, n_index=3, alpha=0.001),
+    3: ft.partial(saturation, n_index=6, alpha=0.001),
+    4: ft.partial(saturation, n_index=6, alpha=0.001)
+}
+
+
+#############################################
+# Manufacture source expressions with sympy #
+#############################################
+x, y = sym.symbols('x[0], x[1]')  # needed by UFL
+t = sym.symbols('t', positive=True)
+
+p_e_sym = {
+    1: {'wetting': 1.0 - (1.0 + t*t)*(10.0 + x*x + (y-5.0)*(y-5.0)),
+        'nonwetting': - 2 - t*(1 + (y-5.0) + x**2)**2 -sym.sqrt(2+t**2)*(1 + (y-5.0)) },
+    2: {'wetting': 1.0 - (1.0 + t*t)*(10.0 + x*x + (y-5.0)*(y-5.0)),
+        'nonwetting': - 2 - t*(1 + (y-5.0) + x**2)**2 -sym.sqrt(2+t**2)*(1 + (y-5.0))},
+    3: {'wetting': 1.0 - (1.0 + t*t)*(10.0 + x*x + (y-5.0)*(y-5.0)*3*sym.sin(-2*t+2*x)*sym.sin(1/2*y-1.2*t)),
+        'nonwetting': - 2 - t*(1 + x**2)**2 -sym.sqrt(2+t**2)},
+    4: {'wetting': 1.0 - (1.0 + t*t)*(10.0 + x*x + (y-5.0)*(y-5.0)*3*sym.sin(-2*t+2*x)*sym.sin(1/2*y-1.2*t)),
+        'nonwetting': - 2 - t*(1 + x**2)**2 -sym.sqrt(2+t**2)}
+}
+
+pc_e_sym = {
+    1: p_e_sym[1]['nonwetting'] - p_e_sym[1]['wetting'],
+    2: p_e_sym[2]['nonwetting'] - p_e_sym[2]['wetting'],
+    3: p_e_sym[3]['nonwetting'] - p_e_sym[3]['wetting'],
+    4: p_e_sym[4]['nonwetting'] - p_e_sym[4]['wetting']
+}
+
+# turn above symbolic code into exact solution for dolphin and
+# construct the rhs that matches the above exact solution.
+dtS = dict()
+div_flux = dict()
+source_expression = dict()
+exact_solution = dict()
+initial_condition = dict()
+for subdomain, isR in isRichards.items():
+    dtS.update({subdomain: dict()})
+    div_flux.update({subdomain: dict()})
+    source_expression.update({subdomain: dict()})
+    exact_solution.update({subdomain: dict()})
+    initial_condition.update({subdomain: dict()})
+    if isR:
+        subdomain_has_phases = ["wetting"]
+    else:
+        subdomain_has_phases = ["wetting", "nonwetting"]
+
+    # conditional for S_pc_prime
+    pc = pc_e_sym[subdomain]
+    dtpc = sym.diff(pc, t, 1)
+    dxpc = sym.diff(pc, x, 1)
+    dypc = sym.diff(pc, y, 1)
+    S = sym.Piecewise((S_pc_sym[subdomain](pc), pc > 0), (1, True))
+    dS = sym.Piecewise((S_pc_sym_prime[subdomain](pc), pc > 0), (0, True))
+    for phase in subdomain_has_phases:
+        # Turn above symbolic expression for exact solution into c code
+        exact_solution[subdomain].update(
+            {phase: sym.printing.ccode(p_e_sym[subdomain][phase])}
+            )
+        # save the c code for initial conditions
+        initial_condition[subdomain].update(
+            {phase: sym.printing.ccode(p_e_sym[subdomain][phase].subs(t, 0))}
+            )
+        if phase == "nonwetting":
+            dS = -dS
+        dtS[subdomain].update(
+            {phase: porosity[subdomain]*dS*dtpc}
+            )
+        pa = p_e_sym[subdomain][phase]
+        dxpa = sym.diff(pa, x, 1)
+        dxdxpa = sym.diff(pa, x, 2)
+        dypa = sym.diff(pa, y, 1)
+        dydypa = sym.diff(pa, y, 2)
+        mu = viscosity[subdomain][phase]
+        ka = relative_permeability[subdomain][phase]
+        dka = ka_prime[subdomain][phase]
+        rho = densities[subdomain][phase]
+        g = gravity_acceleration
+
+        if phase == "nonwetting":
+            # x part of div(flux) for nonwetting
+            dxdxflux = -1/mu*dka(1-S)*dS*dxpc*dxpa + 1/mu*dxdxpa*ka(1-S)
+            # y part of div(flux) for nonwetting
+            dydyflux = -1/mu*dka(1-S)*dS*dypc*(dypa - rho*g) \
+                + 1/mu*dydypa*ka(1-S)
+        else:
+            # x part of div(flux) for wetting
+            dxdxflux = 1/mu*dka(S)*dS*dxpc*dxpa + 1/mu*dxdxpa*ka(S)
+            # y part of div(flux) for wetting
+            dydyflux = 1/mu*dka(S)*dS*dypc*(dypa - rho*g) + 1/mu*dydypa*ka(S)
+        div_flux[subdomain].update({phase: dxdxflux + dydyflux})
+        contructed_rhs = dtS[subdomain][phase] - div_flux[subdomain][phase]
+        source_expression[subdomain].update(
+            {phase: sym.printing.ccode(contructed_rhs)}
+            )
+        # print(f"source_expression[{subdomain}][{phase}] =", source_expression[subdomain][phase])
+
+# Dictionary of dirichlet boundary conditions.
+dirichletBC = dict()
+# similarly to the outer boundary dictionary, if a patch has no outer boundary
+# None should be written instead of an expression.
+# This is a bit of a brainfuck:
+# dirichletBC[ind] gives a dictionary of the outer boundaries of subdomain ind.
+# Since a domain patch can have several disjoint outer boundary parts, the
+# expressions need to get an enumaration index which starts at 0.
+# So dirichletBC[ind][j] is the dictionary of outer dirichlet conditions of
+# subdomain ind and boundary part j.
+# Finally, dirichletBC[ind][j]['wetting'] and dirichletBC[ind][j]['nonwetting']
+# return the actual expression needed for the dirichlet condition for both
+# phases if present.
+
+# subdomain index: {outer boudary part index: {phase: expression}}
+for subdomain in isRichards.keys():
+    if outer_boundary_def_points[subdomain] is None:
+        dirichletBC.update({subdomain: None})
+    else:
+        dirichletBC.update({subdomain: dict()})
+    # if subdomain has no outer boundary, outer_boundary_def_points[subdomain] is None
+
+    if outer_boundary_def_points[subdomain] is not None:
+        # set the dirichlet conditions to be the same code as exact solution on
+        # the subdomain.
+        for outer_boundary_ind in outer_boundary_def_points[subdomain].keys():
+            dirichletBC[subdomain].update(
+                {outer_boundary_ind: exact_solution[subdomain]}
+                )
+
+write_to_file = {
+    'meshes_and_markers': True,
+    'L_iterations': True
+}
+
+# initialise LDD simulation class
+simulation = ldd.LDDsimulation(tol=1E-14, debug=False, LDDsolver_tol=1E-9)
+simulation.set_parameters(output_dir="./output/",
+                          subdomain_def_points=subdomain_def_points,
+                          isRichards=isRichards,
+                          interface_def_points=interface_def_points,
+                          outer_boundary_def_points=outer_boundary_def_points,
+                          adjacent_subdomains=adjacent_subdomains,
+                          mesh_resolution=mesh_resolution,
+                          viscosity=viscosity,
+                          porosity=porosity,
+                          L=L,
+                          lambda_param=lambda_param,
+                          relative_permeability=relative_permeability,
+                          saturation=sat_pressure_relationship,
+                          starttime=starttime,
+                          number_of_timesteps=number_of_timesteps,
+                          number_of_timesteps_to_analyse=number_of_timesteps_to_analyse,
+                          timestep_size=timestep_size,
+                          sources=source_expression,
+                          initial_conditions=initial_condition,
+                          dirichletBC_expression_strings=dirichletBC,
+                          exact_solution=exact_solution,
+                          densities=densities,
+                          include_gravity=True,
+                          write2file=write_to_file,
+                          )
+
+simulation.initialise()
+# print(simulation.__dict__)
+simulation.run()
+# simulation.LDDsolver(time=0, debug=True, analyse_timestep=True)
+# df.info(parameters, True)
diff --git a/layered-soil-case/layered_soil.py b/layered-soil-case/layered_soil.py
deleted file mode 100755
index 952d6e66d70c1f04df2727eb3a549fbbb6431658..0000000000000000000000000000000000000000
--- a/layered-soil-case/layered_soil.py
+++ /dev/null
@@ -1,134 +0,0 @@
-#!/usr/bin/python3
-"""This program sets up a domain together with a decomposition into subdomains
-modelling layered soil. This is used for our LDD article with tp-tp and tp-r
-coupling.
-
-Along with the subdomains and the mesh domain markers are set upself.
-The resulting mesh is saved into files for later use.
-"""
-
-#!/usr/bin/python3
-import dolfin as df
-import mshr
-import numpy as np
-import sympy as sym
-import typing as tp
-import domainPatch as dp
-import LDDsimulation as ldd
-
-# global domain
-subdomain0_vertices = [df.Point(0.0,0.0), #
-                        df.Point(13.0,0.0),#
-                        df.Point(13.0,8.0),#
-                        df.Point(0.0,8.0)]
-
-interface12_vertices = [df.Point(0.0, 7.0),
-                        df.Point(9.0, 7.0),
-                        df.Point(10.5, 7.5),
-                        df.Point(12.0, 7.0),
-                        df.Point(13.0, 6.5)]
-# subdomain1.
-subdomain1_vertices = [interface12_vertices[0],
-                        interface12_vertices[1],
-                        interface12_vertices[2],
-                        interface12_vertices[3],
-                        interface12_vertices[4], # southern boundary, 12 interface
-                        df.Point(13.0, 8.0), # eastern boundary, outer boundary
-                        df.Point(0.0, 8.0) ] # northern boundary, outer on_boundary
-
-# interface23
-interface23_vertices = [df.Point(0.0, 5.0),
-                        df.Point(3.0, 5.0),
-                        df.Point(6.5, 4.5),
-                        df.Point(9.5, 5.0),
-                        df.Point(11.5, 3.5),
-                        df.Point(13.0, 3)]
-
-#subdomain1
-subdomain2_vertices = [interface23_vertices[0],
-                        interface23_vertices[1],
-                        interface23_vertices[2],
-                        interface23_vertices[3],
-                        interface23_vertices[4],
-                        interface23_vertices[5], # southern boundary, 23 interface
-                        subdomain1_vertices[4], # eastern boundary, outer boundary
-                        subdomain1_vertices[3],
-                        subdomain1_vertices[2],
-                        subdomain1_vertices[1],
-                        subdomain1_vertices[0] ] # northern boundary, 12 interface
-
-# interface34
-interface34_vertices = [df.Point(0.0, 2.0),
-                        df.Point(4.0, 2.0),
-                        df.Point(9.0, 2.5),
-                        df.Point(10.5, 2.0),
-                        df.Point(13.0, 1.5)]
-
-# subdomain3
-subdomain3_vertices = [interface34_vertices[0],
-                        interface34_vertices[1],
-                        interface34_vertices[2],
-                        interface34_vertices[3],
-                        interface34_vertices[4], # southern boundary, 34 interface
-                        subdomain2_vertices[5], # eastern boundary, outer boundary
-                        subdomain2_vertices[4],
-                        subdomain2_vertices[3],
-                        subdomain2_vertices[2],
-                        subdomain2_vertices[1],
-                        subdomain2_vertices[0] ] # northern boundary, 23 interface
-
-# subdomain4
-subdomain4_vertices = [df.Point(0.0, 0.0),
-                        df.Point(13.0, 0.0), # southern boundary, outer boundary
-                        subdomain3_vertices[4],# eastern boundary, outer boundary
-                        subdomain3_vertices[3],
-                        subdomain3_vertices[2],
-                        subdomain3_vertices[1],
-                        subdomain3_vertices[0] ] # northern boundary, 34 interface
-
-subdomain_vertices = [subdomain0_vertices,#
-                      subdomain1_vertices,#
-                      subdomain2_vertices,#
-                      subdomain3_vertices,#
-                      subdomain4_vertices]
-# subdomain_vertices = [subdomain0_vertices,#
-#                       subdomain1_vertices,#
-#                       subdomain2_vertices]
-
-
-# interface_vertices introduces a global numbering of interfaces.
-interface_vertices = [interface12_vertices, interface23_vertices, interface34_vertices]
-adjacent_subdomains = [[1,2], [2,3], [3,4]]
-# adjacent_subdomains = [[1,2]]
-# interface_vertices = [interface12_vertices]
-# initialise LDD simulation class
-simulation = ldd.LDDsimulation()
-simulation._init_meshes_and_markers(subdomain_vertices, mesh_resolution=2)
-# subdomain marker functions
-domain_marker = simulation.domain_marker
-mesh_subdomain = simulation.mesh_subdomain
-simulation._init_interfaces(interface_vertices, adjacent_subdomains)
-
-interface = simulation.interface
-interface_marker = simulation.interface_marker
-
-
-# Save mesh to file
-df.File('./domain_layered_soil.xml.gz') << mesh_subdomain[0]
-df.File('./global_interface_marker.pvd') << interface_marker
-#df.File('./subdomain1.xml.gz') << mesh_subdomain
-df.File('./domain_markers.pvd') << domain_marker
-#df.File('./subdomain_boundary_markers.pvd') << subdomain_boundary_marker
-
-
-
-# Save sub domains to file
-#file = File("subdomains_layered_soil.xml")
-#file << subdomains
-
-#file_double = File("subdomains_double.xml")
-#file_double << subdomains_double
-
-# Save sub domains to VTK files
-#file = File("subdomains_layered_soil.pvd")
-#file << subdomains