Pointwise error estimates for 𝐶⁰ interior penalty approximation of biharmonic problems

The aim of this paper is to derive pointwise global and local best approximation type error estimates for biharmonic problems using the C 0 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.