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A conforming finite element method for overlapping and nonmatching grids


Authors: Yunqing Huang and Jinchao Xu
Journal: Math. Comp. 72 (2003), 1057-1066
MSC (2000): Primary 65F10, 65N30
DOI: https://doi.org/10.1090/S0025-5718-02-01459-X
Published electronically: November 18, 2002
MathSciNet review: 1972727
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Abstract: In this paper we propose a finite element method for nonmatching overlapping grids based on the partition of unity. Both overlapping and nonoverlapping cases are considered. We prove that the new method admits an optimal convergence rate. The error bounds are in terms of local mesh sizes and they depend on neither the overlapping size of the subdomains nor the ratio of the mesh sizes from different subdomains. Our results are valid for multiple subdomains and any spatial dimensions.


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Additional Information

Yunqing Huang
Affiliation: Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, Peoples Republic of China, 411105
Email: huangyq@mail.xtu.edu.cn

Jinchao Xu
Affiliation: Center for Computational Mathematics and Applications Pennsylvania State University, University Park, Pennsylvania 16803
Email: xu@math.psu.edu, http:////www.math.psu.edu/xu

DOI: https://doi.org/10.1090/S0025-5718-02-01459-X
Keywords: Nonmatching grid, partition of unity, finite element, overlapping, domain decomposition, mortar
Received by editor(s): May 30, 2001
Received by editor(s) in revised form: November 7, 2001
Published electronically: November 18, 2002
Additional Notes: The work was subsidized by the special funds for Major State Basic Research Projects through Xiangtan University, PRC, and partially supported by NSF DMS-0074299 through Pennsylvania State University and the Center for Computational Mathematics and Applications
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society