Multipoint flux mixed finite element methods for slightly compressible flow in porous media

Abstract

In this paper, we consider multipoint flux mixed finite element discretizations for slightly compressible Darcy flow in porous media. The methods are formulated on general meshes composed of triangles, quadrilaterals, tetrahedra or hexahedra. An inexact Newton method that allows for local velocity elimination is proposed for the solution of the nonlinear fully discrete scheme. We derive optimal error estimates for both the scalar and vector unknowns in the semidiscrete formulation. Numerical examples illustrate the convergence behaviour of the methods, and their performance on test problems including permeability coefficients with increasing heterogeneity.