diff --git a/web/content/docs/benchmarks/elliptic/groundwater-flow-dirichlet-volumetric-source-term.pandoc b/web/content/docs/benchmarks/elliptic/groundwater-flow-dirichlet-volumetric-source-term.pandoc
index 50905f96bde94a073e0204333462c4502108eba1..817882663e73160fd3c4f0846276de21e17e71a5 100644
--- a/web/content/docs/benchmarks/elliptic/groundwater-flow-dirichlet-volumetric-source-term.pandoc
+++ b/web/content/docs/benchmarks/elliptic/groundwater-flow-dirichlet-volumetric-source-term.pandoc
@@ -20,7 +20,7 @@ aliases = [ "/docs/benchmarks/" ] # First benchmark page
We start with Poisson equation:
$$
\begin{equation}
-k\; \Delta p = Q \quad \text{in }\Omega
+- k\; \Delta p = Q \quad \text{in }\Omega
\end{equation}$$
w.r.t boundary conditions
$$
@@ -36,26 +36,25 @@ where $p$ could be the pressure, the subscripts $D$ and $N$ denote the Dirichlet
We solve the Poisson equation on a square domain $[0\times 1]^2$ with $k = 1$ w.r.t. the specific boundary conditions:
$$
\eqalign{
-p(x,y) = 2 &\quad \text{on } (x=0,y) \subset \Gamma_D,\cr
-p(x,y) = 1 &\quad \text{on } (x=1,y) \subset \Gamma_D,\cr
+p(x,y) = 1 &\quad \text{on } (x=0,y) \subset \Gamma_D,\cr
+p(x,y) = 0 &\quad \text{on } (x=1,y) \subset \Gamma_D,\cr
k\;{\partial p(x,y) \over \partial n} = 0 &\quad \text{on }\Gamma_N.
}$$
and the source term is $Q=1$.
The solution of this problem is
$$
-p(x,y) = - \frac{1}{2} (x^2 + x) + 2.
+p(x,y) = - \frac{1}{2} (x^2 + x) + 1.
$$
## Input files
-The main project file is `square_1e2_volumetricsourceterm.prj`. It describes the
+The main project file is
+[`square_1e2_volumetricsourceterm.prj`](https://github.com/ufz/ogs/blob/master/Tests/Data/Elliptic/square_1x1_GroundWaterFlow/square_1e2_volumetricsourceterm.prj). It describes the
processes to be solved and the related process variables together with their
initial and boundary conditions. It also references the bulk mesh and the
boundary meshes associated with the bulk mesh.
-The input mesh `square_1x1_quad_1e2.vtu` is stored in the VTK file format and can be directly visualized in Paraview for example.
-
## Running simulation
To start the simulation (after successful compilation) run:
@@ -63,11 +62,11 @@ To start the simulation (after successful compilation) run:
$ ogs square_1e2_volumetricsourceterm.prj
```
-It will produce some output and write the computed result into the
+OGS writes the computed results (pressure, darcy velocity) into the output file
`square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000.vtu`, which can be
directly visualized and analysed in paraview for example.
-The output on the console will be similar to the following on:
+The output on the console will be similar to:
```
info: ConstantParameter: K
info: ConstantParameter: p0
@@ -76,36 +75,40 @@ info: ConstantParameter: p_Dirichlet_right
info: ConstantParameter: volumetric_source_term_parameter
info: Initialize processes.
info: Solve processes.
-info: [time] Output of timestep 0 took 0.000408888 s.
+info: [time] Output of timestep 0 took 0.000145912 s.
info: === Time stepping at step #1 and time 1 with step size 1
-info: [time] Assembly took 0.000366926 s.
-info: [time] Applying Dirichlet BCs took 3.76701e-05 s.
+info: [time] Assembly took 0.000147104 s.
+info: [time] Applying Dirichlet BCs took 1.81198e-05 s.
info: ------------------------------------------------------------------
info: *** Eigen solver computation
info: -> solve with CG (precon DIAGONAL)
-info: iteration: 9/10000
-info: residual: 7.661918e-17
+info: iteration: 11/10000
+info: residual: 3.965614e-17
info: ------------------------------------------------------------------
-info: [time] Linear solver took 0.000194073 s.
-info: [time] Iteration #1 took 0.000657082 s.
-info: [time] Solving process #0 took 0.000686884 s in time step #1
-info: [time] Time step #1 took 0.000750065 s.
-info: [time] Output of timestep 1 took 0.000280857 s.
+info: [time] Linear solver took 7.79629e-05 s.
+info: [time] Iteration #1 took 0.000268221 s.
+info: [time] Solving process #0 took 0.000288963 s in time step #1
+info: [time] Time step #1 took 0.000308037 s.
+info: [time] Output of timestep 1 took 0.000105858 s.
info: The whole computation of the time stepping took 1 steps, in which
the accepted steps are 1, and the rejected steps are 0.
-info: [time] Execution took 0.0493069 s.
-info: OGS terminated on 2018-09-25 08:00:58+020
+info: [time] Execution took 0.00692892 s.
+info: OGS terminated on 2018-10-12 06:30:13+020
```
## Results and evaluation
### Comparison of the analytical solution and the computed solution
+The numerical solution shown in the following picture is almost a linear
+gradient:
+{{< img src="../square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_VolumetricSourceTerm.png" >}}
+The line plot along the $x$ axis shows that the solution is a quadratic
+function and is in very good agreement to the analytical solution:
{{< img src="../square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
-There is no visible difference between the computed pressure and the analytical
-solution.
-{{< img src="../square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
-The difference between the pressure and the analytical solution is the range of
-machine accuracy.
+
+The difference between the computed solution and the analytical solution is in
+the range of machine precision and therefore almost negligible:
+{{< img src="../square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png" >}}
diff --git a/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
deleted file mode 100644
index ab8c1bb643872e7a4470e8065e68906c635cc841..0000000000000000000000000000000000000000
--- a/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
+++ /dev/null
@@ -1,3 +0,0 @@
-version https://git-lfs.github.com/spec/v1
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diff --git a/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
index ee61773b549609b6a470bcaed49e390ab3de7898..75729a09abe0651dd68cf1bb7037ef6940735583 100644
--- a/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
+++ b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
@@ -1,3 +1,3 @@
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-size 11378
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+size 18173
diff --git a/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_VolumetricSourceTerm.png b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_VolumetricSourceTerm.png
new file mode 100644
index 0000000000000000000000000000000000000000..f494f6c3a3aed077eafaabe785e3934e5a0cd76f
--- /dev/null
+++ b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_Pressure_VolumetricSourceTerm.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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+size 12322
diff --git a/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
new file mode 100644
index 0000000000000000000000000000000000000000..cc32e4275232828bcbc2a24cf63b90ea3794b664
--- /dev/null
+++ b/web/content/docs/benchmarks/elliptic/square_1e2_volumetricsourceterm_pcs_0_ts_1_t_1.000000_diff_Pressure_AnalyticalSolution_VolumetricSourceTerm.png
@@ -0,0 +1,3 @@
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+size 60305