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

作者：Li, Zi Cai; Hu, Hsin Yun; Wang, Song^*; Fang, Qing

来源：Applied Numerical Mathematics, 2008, 58(5): 689-704.

DOI：10.1016/j.apnum.2007.02.007

• superconvergence
• solution derivatives
• boundary singularity
• finite difference method
• stretching function
• Shortley-Weller approximation
• Poisson's equation
• 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(h(1.5))-order superconvergence is derived for the solution derivatives in a discrete H 1 norm.

• 出版日期2008-5
• 单位中山大学