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Can a finite element method perform arbitrarily badly?
Author(s):
Ivo
Babuska;
John
E.
Osborn.
Journal:
Math. Comp.
69
(2000),
443-462.
MSC (1991):
Primary 65N15, 65N30
Posted:
February 24, 1999
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Abstract:
In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive procedures cannot improve this slow convergence. We also show that the  -norm and the nodal point errors converge arbitrarily slowly. With the  -norm two cases need to be distinguished, and the usual duality principle does not characterize the error completely. The constructed elliptic problems are one dimensional.
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Additional Information:
Ivo
Babuska
Affiliation:
Texas Institute for Computational and Applied Mathematics, University of Texas at Austin, Austin, TX 78712
John
E.
Osborn
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742
Email:
jeo@math.umd.edu
DOI:
10.1090/S0025-5718-99-01085-6
PII:
S 0025-5718(99)01085-6
Keywords:
Finite element methods,
convergence,
adaptivity,
rough coefficients
Received by editor(s):
May 5, 1998
Posted:
February 24, 1999
Additional Notes:
The first author was supported in part by NSF Grant #DMS-95-01841.
Copyright of article:
Copyright
2000,
American Mathematical Society
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