Convergence of corrected derivative methods for second-order linear partial differential equations

Approximations where the derivatives are corrected so as to satisfy linear completeness on the derivatives are investigated. These techniques are used in particle methods and other mesh-free methods. The basic approximation i s a Shepard interpolant which possesses only constant completeness. The der ivatives are then corrected to meet linear completeness conditions. It is s hown that the resulting methods have order h convergence in the energy and L-2 norms. The proof is subject to an inf-sup condition which is studied nu merically. Numerical studies of the Poisson equation verify the convergence estimates. Copyright (C) 1999 John Wiley & Sons, Ltd.