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

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.

arXiv commentMinor clarifications, added references. Reordering of some figures. To appear in Computational Geosciences, final article available at http://www.springerlink.com

References in corpus (1)

• A finite element method with strong mass conservation for Biot's linear consolidation model

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• Uniformly well-posed hybridized discontinuous Galerkin/hybrid mixed discretizations for Biot's consolidation model
• Fluid-structure interaction with $H(\text{div})$-conforming finite elements
• A uniform and pressure-robust enriched Galerkin method for the Brinkman equations