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(h(1.5))-order superconvergence is derived for the solution derivatives in a discrete H 1 norm. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
|Journal||Applied Numerical Mathematics|
|Publication status||Published - 2008|