Non-Conforming Finite Element Method for the Brinkman Problem

Juho Könnö () and Rolf Stenberg ()
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Juho Könnö: Helsinki University of Technology, Department of Mathematics and Systems Analysis
Rolf Stenberg: Helsinki University of Technology, Department of Mathematics and Systems Analysis

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 515-522 from Springer

Abstract: 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 the Darcy and Stokes models. A dual mixed framework is introduced for the problem, and H(div)-conforming finite elements are used with Nitsche’s method to obtain a stable formulation. We show the formulation to be stable in a mesh-dependent norm for all values of the parameter and introduce a postprocessing scheme for the pressure, which gives optimal convergence for the pressure.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_55

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DOI: 10.1007/978-3-642-11795-4_55

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