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A two-level nonoverlapping Schwarz algorithm for the Stokes problem without primal pressure unknowns

2011; Wiley; Volume: 88; Issue: 13 Linguagem: Inglês

10.1002/nme.3227

1097-0207

Hyea Hyun Kim, Chang-Ock Lee,

Electromagnetic Scattering and Analysis

International Journal for Numerical Methods in EngineeringVolume 88, Issue 13 p. 1390-1410 Research Article A two-level nonoverlapping Schwarz algorithm for the Stokes problem without primal pressure unknowns Hyea Hyun Kim, Corresponding Author Hyea Hyun Kim hyeahyun@gmail.com hhkim@khu.ac.kr Department of Applied Mathematics, Kyung Hee University, Yongin, KoreaDepartment of Applied Mathematics, Kyung Hee University, Yongin, KoreaSearch for more papers by this authorChang-Ock Lee, Chang-Ock Lee Department of Mathematical Sciences, KAIST, Daejeon, KoreaSearch for more papers by this author Hyea Hyun Kim, Corresponding Author Hyea Hyun Kim hyeahyun@gmail.com hhkim@khu.ac.kr Department of Applied Mathematics, Kyung Hee University, Yongin, KoreaDepartment of Applied Mathematics, Kyung Hee University, Yongin, KoreaSearch for more papers by this authorChang-Ock Lee, Chang-Ock Lee Department of Mathematical Sciences, KAIST, Daejeon, KoreaSearch for more papers by this author First published: 17 May 2011 https://doi.org/10.1002/nme.3227Citations: 8Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract A two-level nonoverlapping Schwarz algorithm is developed for the Stokes problem. The main feature of the algorithm is that a mixed problem with both velocity and pressure unknowns is solved with a balancing domain decomposition by constraints (BDDC)-type preconditioner, which consists of solving local Stokes problems and one global coarse problem related to only primal velocity unknowns. Our preconditioner allows to use a smaller set of primal velocity unknowns than other BDDC preconditioners without much concern on certain flux conditions on the subdomain boundaries and the inf–sup stability of the coarse problem. In the two-dimensional case, velocity unknowns at subdomain corners are selected as the primal unknowns. In addition to them, averages of each velocity component across common faces are employed as the primal unknowns for the three-dimensional case. By using its close connection to the Dual–primal finite element tearing and interconnecting (FETI-DP algorithm) (SIAM J Sci Comput 2010; 32: 3301–3322; SIAM J Numer Anal 2010; 47: 4142–4162], it is shown that the resulting matrix of our algorithm has the same eigenvalues as the FETI-DP algorithm except zero and one. The maximum eigenvalue is determined by H/h, the number of elements across each subdomains, and the minimum eigenvalue is bounded below by a constant, which does not depend on any mesh parameters. Convergence of the method is analyzed and numerical results are included. Copyright © 2011 John Wiley & Sons, Ltd. Citing Literature Volume88, Issue1330 December 2011Pages 1390-1410 RelatedInformation