The Influence of the Boundary Discretization on theMultipoint Flux Approximation L-method

In this work, the convergence of multipoint flux approximations is investigated using a benchmark problem. Of special interest is the recently (in [AAV ss]) introduced L-method. We show how important it is for this new method to handle Dirichlet boundary conditions in a suitable way. Following the original approach of combining Oand L-method on the two half edges close to the boundary, it turns out that the superconvergence might be lost. As an alternative approach we propose using the O-method on both half edges. This simple modification can significantly improve the numerical results.