A Dual–Mixed Finite Element Method for the Brinkman Problem

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

doi:10.5802/smai-jcm.7

Howell, Jason S.¹ ; Neilan, Michael ² ; Walkington, Noel J.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, Tome 2 (2016), pp. 1-17.

Résumé

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.

Publié le : 2016-09-05

MR Zbl

DOI : 10.5802/smai-jcm.7

Classification : 65N30, 65N12
Mots clés : Brinkman, Stokes, Darcy, mixed methods

Affiliations des auteurs :

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

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     title = {A {Dual{\textendash}Mixed} {Finite} {Element} {Method} for the {Brinkman} {Problem}},
     journal = {The SMAI Journal of computational mathematics},
     pages = {1--17},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {2},
     year = {2016},
     doi = {10.5802/smai-jcm.7},
     mrnumber = {3633543},
     zbl = {1416.76112},
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Howell, Jason S.; Neilan, Michael; Walkington, Noel J. A Dual–Mixed Finite Element Method for the Brinkman Problem. The SMAI Journal of computational mathematics, Tome 2 (2016), pp. 1-17. doi : 10.5802/smai-jcm.7. http://www.numdam.org/articles/10.5802/smai-jcm.7/

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