Can a finite element method

perform arbitrarily badly?

Authors:
Ivo Babuska and John E. Osborn

Journal:
Math. Comp. **69** (2000), 443-462

MSC (1991):
Primary :, 65N15, 65N30

DOI:
https://doi.org/10.1090/S0025-5718-99-01085-6

Published electronically:
February 24, 1999

MathSciNet review:
1648351

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-99-01085-6

Keywords:
Finite element methods,
convergence,
adaptivity,
rough coefficients

Received by editor(s):
May 5, 1998

Published electronically:
February 24, 1999

Additional Notes:
The first author was supported in part by NSF Grant #DMS-95-01841.

Article copyright:
© Copyright 2000
American Mathematical Society