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

Authors:
Zi-Cai Li;Hsin-Yun Hu;Song Wang;Qing Fang
Affiliations:
Department of Applied Mathematics and Department of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan 80424;Department of Mathematics, Tung-Hai University, TaiChung, Taiwan;School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia;Department of Mathematical Sciences, Faculty of Science, Yamagata University, Yamagata 990-8560, Japan
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

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.