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A robust nonconforming  -element
Author(s):
Trygve
K.
Nilssen;
Xue-Cheng
Tai;
Ragnar
Winther.
Journal:
Math. Comp.
70
(2001),
489-505.
MSC (2000):
Primary 65N12, 65N30
Posted:
February 23, 2000
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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  -element which is  -conforming. We show that the new finite element method converges in the energy norm uniformly in the perturbation parameter.
References:
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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:
10.1090/S0025-5718-00-01230-8
PII:
S 0025-5718(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
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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