Porous Media Group
MSc project

Exact and Superconvergent Solutions of the Multi-Point Flux Approximation O-method: Analysis and Numerical Tests, 2014

Daniel Olderkjær

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Advisors: Jan M. Nordbotten, Eirik Keilegavlen, Florin Radu

Short description of project:

In this thesis we prove the multi-point flux approximation O-method (MPFA) to yield exact potential and flux for the trigonometric potential functions u(x,y)=sin(x)sin(y) and u(x,y)=cos(x)cos(y). This is done on uniform square grids in a homogeneous medium with principal directions of the permeability aligned with the grid directions when having periodic boundary conditions. We wanted to gain new insight into the convergence of the method, as well as to develop theoretical proofs for what seems as decent examples for testing implementation.

Link to thesis at BORA-UiB: Link