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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

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Partition of unity method on nonmatching grids for the Stokes problem

C. Bacuta / J. Chen / Y. Huang / J. Xu§ / L. Zikatanov§

Mathematical Sciences, University of Delaware, Newark, DE, 19716

School of Mathematics and Computer Science, Nanjing Normal University Nanjing, 210097, Peoples Republic of China

Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, Peoples Republic of China, 411105

§ Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Citation Information: Journal of Numerical Mathematics jnma. Volume 13, Issue 3, Pages 157–169, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/156939505774286148, September 2005

We consider the Stokes problem on a plane polygonal domain We propose a finite element method for overlapping or nonmatching grids for the Stokes problem based on the partition of unity method. We prove that the discrete inf-sup condition holds with a constant independent of the overlapping size of the subdomains. The results are valid for multiple subdomains and any spatial dimension.

Key Words: non-matching grid,; finite element method,; partition of unity,; Stokes problem

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