H(div)-conforming finite elements for the brinkman problem

Juho Könnö*, Rolf Stenberg

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

29 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2227-2248
Number of pages22
JournalMathematical Models and Methods in Applied Sciences
Volume21
Issue number11
DOIs
Publication statusPublished - Nov 2011
MoE publication typeA1 Journal article-refereed

Keywords

  • a posteriori error estimates
  • Brinkman problem
  • DarcyStokes equation
  • H(div)-conforming
  • Nitsche's method
  • postprocessing
  • SIPG

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