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A weighted least squares finite element method for elliptic problems with degenerate and singular coefficients


Authors: S. Bidwell, M. E. Hassell and C. R. Westphal
Journal: Math. Comp. 82 (2013), 673-688
MSC (2010): Primary 65N30, 65N15, 35J70
DOI: https://doi.org/10.1090/S0025-5718-2012-02659-7
Published electronically: December 4, 2012
MathSciNet review: 3008834
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Abstract: We consider second order elliptic partial differential equations with coefficients that are singular or degenerate at an interior point of the domain. This paper presents formulation and analysis of a novel weighted-norm least squares finite element method for this class of problems. We propose a weighting scheme that eliminates the pollution effect and recovers optimal convergence rates. Theoretical results are carried out in appropriately weighted Sobolev spaces and include ellipticity bounds on the weighted homogeneous least squares functional, regularity bounds on the elliptic operator, and error estimates. Numerical experiments confirm the predicted error bounds.


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Additional Information

S. Bidwell
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Email: bidwell.stephen@gmail.com

M. E. Hassell
Affiliation: Department of Mathematics, Binghamton University, Binghamton, New York 13902-6000
Email: hassell.matthew@gmail.com

C. R. Westphal
Affiliation: Department of Mathematics and Computer Science, Wabash College, P.O. Box 352, Crawfordsville, Indiana 47933
Email: westphac@wabash.edu

DOI: https://doi.org/10.1090/S0025-5718-2012-02659-7
Received by editor(s): August 31, 2010
Received by editor(s) in revised form: May 27, 2011, and October 5, 2011
Published electronically: December 4, 2012
Additional Notes: The research in this paper was supported by National Science Foundation Grant DMS-0755260.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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