Convergence of consistent and inconsistent finite difference schemes and an acceleration technique (Q1602821)

The author states and generalizes in part some recent on finite difference methods for Dirichlet problems in a bounded domain \(\Omega\) which the author has obtained by himself or with coworkers. After stating a superconvergence property of the finite difference solution for the case where the exact solution \(u\) belongs to \(C^4(\overline\Omega)\), the author remarks that such a property does not hold in general if \(u\) not belongs to \(C^4(\overline\Omega)\). Next, he gives a convergence theorem for an inconsistent scheme under some assumptions. Furthermore, he tells us that the accuracy of the approximate solution can be improved by a coordinate transformation and gives us a numerical example.