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Pointwise error estimates for $ C^0$ interior penalty approximation of biharmonic problems


Author: D. Leykekhman
Journal: Math. Comp. 90 (2021), 41-63
MSC (2020): Primary 65N30, 65N15
DOI: https://doi.org/10.1090/mcom/3596
Published electronically: October 8, 2020
MathSciNet review: 4166452
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Abstract: The aim of this paper is to derive pointwise global and local best approximation type error estimates for biharmonic problems using the $ C^0$ interior penalty method. The analysis uses the technique of dyadic decompositions of the domain, which is assumed to be a convex polygon. The proofs require local energy estimates and new pointwise Green's function estimates for the continuous problem which has independent interest.


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Additional Information

D. Leykekhman
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: dmitriy.leykekhman@uconn.edu

DOI: https://doi.org/10.1090/mcom/3596
Keywords: Maximum norm, finite element method, pointwise error estimates, Green's function, biharmonic equation, interior penalty, local error estimates
Received by editor(s): July 21, 2019
Received by editor(s) in revised form: August 16, 2020, and August 29, 2020
Published electronically: October 8, 2020
Additional Notes: The author was partially supported by NSF grant DMS-1913133.
Article copyright: © Copyright 2020 American Mathematical Society