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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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A robust nonconforming $H^2$-element
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by Trygve K. Nilssen, Xue-Cheng Tai and Ragnar Winther PDF
Math. Comp. 70 (2001), 489-505 Request permission

Abstract:

Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample is given to show that the Morley method diverges for the reduced second order equation. As an alternative to the Morley element we propose to use a nonconforming $H^2$-element which is $H^1$-conforming. We show that the new finite element method converges in the energy norm uniformly in the perturbation parameter.
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Additional Information
  • Trygve K. Nilssen
  • Affiliation: Department of Mathematics, University of Bergen, Johannes Brunsgt. 12, 5007 Bergen, Norway
  • Email: Trygve.Nilssen@mi.uib.no
  • Xue-Cheng Tai
  • Affiliation: Department of Mathematics, University of Bergen, Johannes Brunsgt. 12, 5007 Bergen, Norway
  • Email: Xue-Cheng.Tai@mi.uib.no
  • Ragnar Winther
  • Affiliation: Department of Informatics and Department of Mathematics, University of Oslo, P.O. Box 1080 Blindern, 0316 Oslo, Norway
  • MR Author ID: 183665
  • Email: ragnar@ifi.uio.no
  • Received by editor(s): March 9, 1999
  • Received by editor(s) in revised form: June 8, 1999
  • Published electronically: February 23, 2000
  • Additional Notes: This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431, and by ELF Petroleum Norway AS
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 489-505
  • MSC (2000): Primary 65N12, 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-00-01230-8
  • MathSciNet review: 1709156