Convergence of consistent and inconsistent finite difference schemes and an acceleration technique

摘要

This paper states and generalizes in part some recent results on finite difference methods for Dirichlet problems in a bounded domain Ω which the author has obtained by himself or with coworkers. After stating a superconvergence property of finite difference solution for the case where the exact solution u belongs to C4(Ω̄), it is remarked that such a property does not hold in general if u∉C4(Ω̄). Next, a convergence theorem is given for inconsistent schemes under some assumptions. Furthermore, it is shown that the accuracy of the approximate solution can be improved by a coordinate transformation. Numerical examples are also given.