This folder contains several Matlab scripts which can be used to evaluate a solution to one of the benchmark cases with the corresponding reference solution.

### 1 Comparison of the solution in the matrix

#### 1.1 Preparation of the solution data

The solution data has to be provided in form of a Matlab `mat`-file which has to contain the following variables:

* `Points`: an `np x 2` matrix that contains the x and y coordinates of the `np` vertices of the employed computational grid in columns `1` and `2`, respectively. 
* `T`: an `nt x nvelem` connectivity matrix which contains in each row the `nvelem` vertex indices with respect to the numbering induced by `Points`.
* `P`: an `nt`-size vector containing the solution value for each cell with respect to the numbering induced by `T`.

The original solution data is available as a VTK file? A helper function `hdf5_to_mat.m` is provided which extracts the required `mat`-file from an HDF5-file, which in turn can be exported from Paraview: select `File` -> `Save Data...` -> `Files of type: Xdmf Data File`, use the produced `h5`-file.

#### 1.2 Performing the comparison

The function [compute_2d_error](compute_2d_error.m) can be used to calculate a relative L2-error of the matrix solution. It has the signature
```
function [relativeMatrixError] = compute_2d_error(coarseFile, referenceFile)
```
`coarseFile` is the `mat`-file explained above, `referenceFile` is one of the `mat`-files found in the `results/mfd`-subfolders, for example `../hydrocoin/results/mfd/mfd_hydrocoin.mat`.