Generalized Clenshaw-Curtis quadrature rule with application to a collocation least-squares method

Abstract

This paper deals with an extension of one-dimensional Clenshaw-Curtis quadrature rule to Rd, d ≥ 2 on a convex domain. As one of its applications, we apply this quadrature rule to a collocation least-squares method using arbitrary abscissas for a first-order system of an elliptic boundary value problem so that the convergence analysis on a numerical solution can be shown in a standard Sobolev norm. © 2007 Elsevier Inc. All rights reserved.