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A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem |
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| Authors: | Blanca Ayuso de Dios Franco Brezzi L Donatella Marini Jinchao Xu Ludmil Zikatanov |
| Affiliation: | 1. Centre de Recerca Matemática, Campus de Bellaterra, 08193, Bellaterra, Barcelona, Spain 2. IUSS-Pavia c/p IMATI-CNR, Via Ferrata 5/A, 27100, Pavia, Italy 3. Department of Mathematics, KAU, PO Box 80203, Jeddah, 21589, Saudi Arabia 4. Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100, Pavia, Italy 5. Department of Mathematics, Penn State University, University Park, PA, 16802, USA |
| Abstract: | In this paper we construct Discontinuous Galerkin approximations of the Stokes problem where the velocity field is $H(\mathrm{div},\Omega )$ -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. |
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