SUPERCONVERGENCE AND NONSUPERCONVERGENCE OF THE SHORTLEY-WELLER APPROXIMATIONS FOR DIRICHLET PROBLEMS
Tetsuro Yamamoto, Qing Fang, Xiaojun Chen · Numerical Functional Analysis and Optimization · 2001
We are concerned with the numerical solutions of Dirichlet problems of elliptic equations. The convergence behavior of numerical solutions by using Shortley-Weller approximation is considered. We give three examples and prove that they have properties of nonsuperconvergence near any boundary point, superconvergence near a side and superconvergence near a corner, respectively.