Convergence Analysis of the Shortley-Weller Method on Refinement Grids for Elliptic Equations with Singularities. (2nd June 2016)

• Record Type: Journal Article
• Authors: Zhang, Xiao-Yu; Wang, Ruyun; Fang, Qing
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 6(2016)
• Page Start: 805
• Page End: 822
• Publication Date: 2016-06-02
• Subjects: Accelerated convergence -- elliptic boundary value problems -- mesh refinement -- Shortley-Weller method -- stretching functions; 65M06 -- 65M12; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1147463
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we consider the convergence problem of the Shortley-Weller method on refinement grids applied to elliptic partial differential equations. The refinement uses polynomial and exponential stretching functions for Dirichlet boundary value problems in a bounded domain Ω whose solutions have singular derivatives near a part or the whole of the boundary of Ω. In the case where Ω is the unit square, it is shown that the methods are convergent and the convergence can be accelerated by varying parameters in the stretching functions. Numerical examples are given to illustrate how the effect on the stretching functions depends upon the choice of parameters.