A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem

Authors:
Blanca Ayuso De Dios;Franco Brezzi;L. Donatella Marini;Jinchao Xu;Ludmil Zikatanov
Affiliations:
Centre de Recerca Matemática, Campus de Bellaterra, Bellaterra, Barcelona, Spain 08193;IUSS-Pavia c/p IMATI-CNR, Pavia, Italy 27100 and Department of Mathematics, KAU, Jeddah, Saudi Arabia 21589;Dipartimento di Matematica, Università di Pavia, Pavia, Italy 27100;Department of Mathematics, Penn State University, University Park, USA 16802;Department of Mathematics, Penn State University, University Park, USA 16802
Venue:
Journal of Scientific Computing
Year:
2014

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Abstract

In this paper we construct Discontinuous Galerkin approximations of the Stokes problem where the velocity field is $$H(\mathrm{div},\Omega )$$H(div,Ω)-conforming. This implies that the velocity solution is divergence-free in the whole domain. This property can be exploited to design a simple and effective preconditioner for the final linear system.