Numerical Computations with H(div)-Finite Elements for the Brinkman Problem

TL;DR

This paper investigates H(div)-conforming finite element methods for the Brinkman problem, extending analysis to variable permeability, introducing hybridization techniques, and demonstrating applications in domain decomposition and adaptive mesh refinement.

Contribution

It introduces a hybridization method for H(div)-finite elements applied to the Brinkman problem, with convergence analysis and practical numerical applications.

Findings

Validated the theoretical a priori and a posteriori error estimates.

Extended the analysis to non-constant permeability.

Demonstrated effectiveness in domain decomposition and adaptive refinement.

Abstract

The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant permeability. A hybridization technique for the problem is presented, complete with a convergence analysis and numerical verification. Finally, the numerical convergence studies are complemented with numerical examples of applications to domain decomposition and adaptive mesh refinement.