Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions

Abstract

This paper presents the MPFA O-method for quadrilateral grids, and gives convergence rates for the potential and the normal velocities. The convergence rates are estimated from numerical experiments. If the potential is in H 1+α , α>0, the found L 2 convergence order on rough grids in physical space is min{2, 2α} for the potential and min{1, α} for the normal velocities. For smooth grids the convergence order for the normal velocities increases to min{2,α}. The O-method is exact for uniform flow on rough grids. This also holds in three dimensions, where the cells may have nonplanar surfaces.