A robust nonconforming -element

Authors:
Trygve K. Nilssen, Xue-Cheng Tai and Ragnar Winther

Journal:
Math. Comp. **70** (2001), 489-505

MSC (2000):
Primary 65N12, 65N30

DOI:
https://doi.org/10.1090/S0025-5718-00-01230-8

Published electronically:
February 23, 2000

MathSciNet review:
1709156

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 -element which is -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

Email:
ragnar@ifi.uio.no

DOI:
https://doi.org/10.1090/S0025-5718-00-01230-8

Keywords:
singular perturbation problems,
nonconforming finite elements,
uniform error estimates.

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

Article copyright:
© Copyright 2000
American Mathematical Society