Analysis and comparison of mixed finite element and multipoint flux approximation methods for homogeneous media

Abstract

We consider discretization on quadrilateral grids of an elliptic operator occurring, for example, in the pressure equation for porous-media flow. In a realistic setting – with non-orthogonal grid, and anisotropic, heterogeneous permeability – special discretization techniques are required. Mixed finite element (MFE) and multipoint flux approximation (MPFA) are two methods that can handle such situations. Previously, a framework for analytical comparison of MFE and MPFA in special cases has been suggested. A comparison of MFE and MPFA-O (one of two main variants of MPFA) for isotropic, homogeneous permeability on a uniformly distorted grid was also performed. In the current paper, we utilize the suggested framework in a slightly different manner to analyze and compare MFE, MPFA-O and MPFA-U (the second main variant of MPFA). We reconsider the case previously analyzed. We also consider the case of generally anisotropic, homogeneous permeability on an orthogonal grid.