Convergence Analysis of the Shortley-Weller Method on Refinement Grids for Elliptic Equations with Singularities. (2nd June 2016) - Zhang, Xiao-Yu; Wang, Ruyun; Fang, Qing
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.