Equal-order finite elements with local projection stabilization for the Darcy-Brinkman equations

Braack, M. and Schieweck, F. (2011) Equal-order finite elements with local projection stabilization for the Darcy-Brinkman equations Computer Methods in Applied Mechanics and Engineering, 200 (9-12). pp. 1126-1136. DOI 10.1016/j.cma.2010.06.034.

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Abstract

For the Darcy-Brinkman equations, which model porous media flow, we present an equal-order H(1)-conforming finite element method for approximating velocity and pressure based on a local projection stabilization technique. The method is stable and accurate uniformly with respect to the coefficients of the viscosity and the zeroth order term in the momentum equation. We prove a priori error estimates in a mesh-dependent norm as well as in the L(2)-norm for velocity and pressure. In particular, we obtain optimal order of convergence in L(2) for the pressure in the Darcy case with vanishing viscosity and for the velocity in the general case with a positive viscosity coefficient. Numerical results for different values of the coefficients in the Darcy-Brinkman model are presented which confirm the theoretical results and indicate nearly optimal order also in cases which are not covered by the theory. (C) 2010 Elsevier B.V. All rights reserved.

Document Type: Article
Keywords: Porous media flow Darcy-Brinkman equations Stokes Equal-order finite elements Local projection stabilization stokes problem oseen problem flow
Research affiliation: Kiel University
Refereed: Yes
DOI etc.: 10.1016/j.cma.2010.06.034
ISSN: 0045-7825
Date Deposited: 01 Nov 2012 04:55
Last Modified: 01 Nov 2012 04:55
URI: http://eprints.uni-kiel.de/id/eprint/16873

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