Sharp estimates for finite element approximations to elliptic problems with Neumann boundary data of low regularity
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- by Aaron Solo;
- Math. Comp. 76 (2007), 1787-1800
- DOI: https://doi.org/10.1090/S0025-5718-07-01993-X
- Published electronically: May 3, 2007
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Abstract:
Consider a second order homogeneous elliptic problem with smooth coefficients, $Au = 0$, on a smooth domain, $\Omega$, but with Neumann boundary data of low regularity. Interior maximum norm error estimates are given for $C^0$ finite element approximations to this problem. When the Neumann data is not in $L^1(\partial \Omega )$, these local estimates are not of optimal order but are nevertheless shown to be sharp. A method for ameliorating this sub-optimality by preliminary smoothing of the boundary data is given. Numerical examples illustrate the findings.References
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Bibliographic Information
- Aaron Solo
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- Address at time of publication: Susquehanna International Group, 401 City Line Avenue, Bala Cynwyd, Pennsylvania 19004
- Email: als54@cornell.edu
- Received by editor(s): April 11, 2006
- Received by editor(s) in revised form: August 2, 2006
- Published electronically: May 3, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 76 (2007), 1787-1800
- MSC (2000): Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-07-01993-X
- MathSciNet review: 2336268