Pointwise error estimates for 𝐶⁰ interior penalty approximation of biharmonic problems

Leykekhman, D.

doi:10.1090/mcom/3596

Pointwise error estimates for $C^0$ interior penalty approximation of biharmonic problems
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by D. Leykekhman;

Math. Comp. 90 (2021), 41-63

DOI: https://doi.org/10.1090/mcom/3596

Published electronically: October 8, 2020

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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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