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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A conforming finite element method for overlapping and nonmatching grids
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by Yunqing Huang and Jinchao Xu PDF
Math. Comp. 72 (2003), 1057-1066 Request permission

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
  • MR Author ID: 228866
  • Email: xu@math.psu.edu
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Math. Comp. 72 (2003), 1057-1066
  • MSC (2000): Primary 65F10, 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-02-01459-X
  • MathSciNet review: 1972727