Mixed Mimetic Spectral Element method applied to Darcy's problem

TL;DR

This paper introduces a mimetic spectral element discretization for Darcy's problem that preserves integral relations exactly, effectively handling anisotropic permeability tensors and demonstrating optimal convergence on test cases.

Contribution

The paper develops a novel mimetic spectral element method for Darcy's problem that accurately discretizes permeability tensors and maintains integral relations exactly.

Findings

Method converges at optimal rate

Effective for anisotropic permeability

Performs well on standard test problems

Abstract

We present a discretization for Darcy's problem using the recently developed Mimetic Spectral Element Method. The gist lies in the exact discrete representation of integral relations. In this paper, an anisotropic flow through a porous medium is considered and a discretization of a full permeability tensor is presented. The performance of the method is evaluated on standard test problems, converging at the same rate as the best possible approximation.