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Volume 9, Issue 4
A Hybrid Mortar Method for Incompressible Flow

H. Egger & C. Waluga

Int. J. Numer. Anal. Mod., 9 (2012), pp. 793-812.

Published online: 2012-09

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  • 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.

  • Keywords

Stokes equations, interface problems, discontinuous Galerkin methods, hybridization, mortar methods, non-matching grids.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-793, author = {H. Egger and C. Waluga}, title = {A Hybrid Mortar Method for Incompressible Flow}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/659.html} }
TY - JOUR T1 - A Hybrid Mortar Method for Incompressible Flow AU - H. Egger & C. Waluga JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 793 EP - 812 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/659.html KW - Stokes equations, interface problems, discontinuous Galerkin methods, hybridization, mortar methods, non-matching grids. AB -

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.

H. Egger and C. Waluga. (2012). A Hybrid Mortar Method for Incompressible Flow. International Journal of Numerical Analysis and Modeling. 9 (4). 793-812. doi:
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