Quadrature for meshless methods

In this paper we discuss quadrature schemes for meshless methods. We consider the Neumann problem and derive an estimate for the energy norm error between the exact solution, u, and the quadrature approximate solution, u(h)*, in terms of a parameter, h, associated with the family of approximation spaces. and quantities eta, tau, and epsilon that measure the errors in the stiffness matrix, in the boundary data, and in the right-hand side vector, respectively, due to the quadrature. The major hypothesis in the estimate is that the quadrature stiffness matrix has zero row sums, a hypothesis that can be easily achieved by a simple correction of the diagonal elements. Copyright (C) 2008 John Wiley & Sons. Ltd.