Pointwise error estimates for C0 interior penalty approximation of biharmonic problems

Abstract

The aim of this paper is to derive pointwise global and local best approximation type error estimates for biharmonic problem using C0 interior penalty method. The analysis uses the technique of dyadic decompositions of the domain, which assumed to be a convex polygon. The proofs require local energy estimate and new pointwise Green’s function estimates for the continuous problem which have an independent interest.