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Journal of Computational Mathematics

A Dual–Mixed Finite Element Method for the Brinkman Problem
Jason S. Howell1; Michael Neilan2; Noel J. Walkington3
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.

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:
DOI: 10.5802/smai-jcm.7
Classification: 65N30, 65N12
Keywords: Brinkman, Stokes, Darcy, mixed methods
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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