Superconvergence of solution derivatives of the Shortley–Weller difference approximation to Poisson's equation with singularities on polygonal domains

This paper presents a superconvergence analysis for the Shortley–Weller finite difference approximation of Poisson's equation with unbounded derivatives on a polygonal domain. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O(h1.5)-order superconvergence is derived for the solution derivatives in a discrete H1 norm.