Stabilized velocity post‐processings for Darcy flow in heterogeneous porous media

Abstract

Stable and accurate finite element methods are presented for Darcy flow in heterogeneous porous media with an interface of discontinuity of the hydraulic conductivity tensor, Accurate velocity fields are computed through global or local post-processing formulations that use previous approximations of the hydraulic potential. Stability is provided by combining Galerkin and least squares (GLS) residuals of the governing equations with an additional stabilization on the interface that incorporates the discontinuity on the tangential component of the velocity field in a strong sense. Numerical analysis is outlined and numerical results are presented to illustrate the good performance of the proposed methods, Convergence studies for a heterogeneous and anisotropic porous medium confirm the same rates of convergence predicted for homogeneous problem with smooth solutions, for both global and local post-processings.