Year: 2012
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 793–812
Abstract
In this paper, we consider the discretization of the Stokes problem on domain partitions with non-matching meshes. We propose a hybrid mortar method, which is motivated by a variational characterization of solutions of the corresponding interface problem. The discretization of the subdomain problems is based on standard inf-sup stable finite element pairs and additional unknowns on the interface. These allow to reduce the coupling between subdomains, which comes from the variational incorporation of interface conditions. The discrete inf-sup stability condition is proven under weak assumptions on the interface mesh, and optimal a-priori error estimates are derived with respect to the energy and $L^2$-norm. The theoretical results are illustrated with numerical tests.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-659
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 793–812
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Stokes equations interface problems discontinuous Galerkin methods hybridization mortar methods non-matching grids.