H(div)-CONFORMING FINITE ELEMENTS FOR THE BRINKMAN PROBLEM

Abstract

The Brinkman equations describe the flow of a viscous fluid in a porous matrix. Mathematically the Brinkman model is a parameter-dependent combination of both the Darcy and Stokes models. We introduce a dual mixed framework for the problem, and use H( div )-conforming finite elements with the symmetric interior penalty Galerkin method to obtain a stable formulation. We show that the formulation is stable in a mesh-dependent norm for all values of the parameter. We also introduce a postprocessing scheme for the pressure along with a residual-based a posteriori estimator, which is shown to be efficient and reliable for all parameter values.