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

Published electronically:
November 18, 2002

MathSciNet review:
1972727

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Abstract | References | Similar Articles | Additional Information

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