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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the convergence properties of the quadrilateral elements of Sander and Beckers
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by Zhong Ci Shi PDF
Math. Comp. 42 (1984), 493-504 Request permission

Abstract:

A class of nonconforming quadrilateral membrane elements, introduced by Sander and Beckers, is discussed in all details. It is proved that two elements that do not pass the patch test may still yield convergence under a suitable condition on mesh subdivisions, whereas one such element is found to be divergent for all mesh subdivisions. All other finite elements in this class that pass the patch test are convergent. The mathematical analysis provides a clear explanation of the convergence behavior appearing in the numerical examples of Sander and Beckers.
References
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 42 (1984), 493-504
  • MSC: Primary 65N30; Secondary 73K25
  • DOI: https://doi.org/10.1090/S0025-5718-1984-0736448-4
  • MathSciNet review: 736448