A Dual–Mixed Finite Element Method for the Brinkman Problem

Jason S. Howell; Michael Neilan; Noel J. Walkington

doi:10.5802/smai-jcm.7

Jason S. Howell ¹; Michael Neilan ²; Noel J. Walkington ³

¹ Department of Mathematics, College of Charleston, Charleston, SC 29424
² Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
³ Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213

The SMAI Journal of computational mathematics, Volume 2 (2016), pp. 1-17.

Abstract

A mixed variational formulation of the Brinkman problem is presented which is uniformly well–posed for degenerate (vanishing) coefficients under the hypothesis that a generalized Poincaré inequality holds. The construction of finite element schemes which inherit this property is then considered.

Published online: 2016-09-04

MR Zbl

DOI: 10.5802/smai-jcm.7

Classification: 65N30, 65N12
Keywords: Brinkman, Stokes, Darcy, mixed methods

Author's affiliations:

Jason S. Howell ¹; Michael Neilan ²; Noel J. Walkington ³

¹ Department of Mathematics, College of Charleston, Charleston, SC 29424
² Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
³ Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213

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Jason S. Howell; Michael Neilan; Noel J. Walkington. A Dual–Mixed Finite Element Method for the Brinkman Problem. The SMAI Journal of computational mathematics, Volume 2 (2016), pp. 1-17. doi : 10.5802/smai-jcm.7. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.7/

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