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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 979307, 18 pages
http://dx.doi.org/10.1155/2012/979307
Research Article

Mixed Mortar Element Method for Element and Its Multigrid Method for the Incompressible Stokes Problem

1Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China
2School of Sciences, Nanjing University of Posts and Telecommunications, Nanjing 210046, China

Received 15 November 2011; Revised 19 April 2012; Accepted 20 April 2012

Academic Editor: Dongdong Ge

Copyright © 2012 Yaqin Jiang and Jinru Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss a mortar-type element method for the incompressible Stokes problem. We prove the inf-sup condition and obtain the optimal error estimate. Meanwhile, we propose a -cycle multigrid for solving this discrete problem and prove the optimal convergence of the multigrid method, that is, the convergence rate is independent of the mesh size and mesh level. Finally, numerical experiments are presented to confirm our theoretical results.