MPFA methods for Richards' equation, 2021

Advisors: Florin A. Radu, Erlend Storvik

Short description of the project:
In this thesis, we review spatial discretization methods for parabolic problems, with applications to Richards’ equation. In particular, we discretize Richards’ equation after Kirchhoff transform with the MPFA-L-method in space, backward Euler in time and L-scheme for linearization. Then, we apply the techniques in (Cao, Helmig, Wohlmuth, 2011) to prove a convergence rate estimate. We also compare the spatial discretization techniques numerically on different grids. Moreover, we do numerical experiments involving the fully discretized Richards’ equation, verifying our theoretical findings. All the numerical experiments are done using our code, implemented with Python and Numpy, see https://github.com/trulsmoholt/masterthesis.

Link to the thesis.