Convergence analysis for a second-order elliptic equation by a collocation method using scattered points

Abstract

A collocation method using scattered points applied to a second-order elliptic differential equation is analyzed by establishing a new quadrature formula for the space of the polynomials. We show that a polynomial solution possesses stability and preserves a similar convergence property occurred in the classical high order collocation method. © 2005 Elsevier B.V. All rights reserved.