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Sharp estimates for finite element approximations to elliptic problems with Neumann boundary data of low regularity


Author: Aaron Solo
Journal: Math. Comp. 76 (2007), 1787-1800
MSC (2000): Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-07-01993-X
Published electronically: May 3, 2007
MathSciNet review: 2336268
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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.


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Additional 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

DOI: https://doi.org/10.1090/S0025-5718-07-01993-X
Keywords: Finite element methods, boundary value problems, low regularity data
Received by editor(s): April 11, 2006
Received by editor(s) in revised form: August 2, 2006
Published electronically: May 3, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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