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Supraconvergence and Supercloseness of a Scheme for Elliptic Equations on Nonun...

In this paper, we study the convergence of a finite difference scheme on nonuniform grids for the solution of second-order elliptic equations with mixed derivatives and variable coefficients in polygonal domains subjected to Dirichlet boundary conditions. We show that the scheme is equivalent to a fully discrete linear finite element approximation with quadrature. It exhibits the phenomenon of supraconvergence,...

Superconvergence of the gradient in a fully discrete FEM scheme: one-dimensiona...

On the supraconvergence of elliptic finite difference schemes

This paper deals with the supraconvergence of elliptic finite difference schemes on variable grids for second order elliptic boundary value problems subject to Dirichlet boundary conditions in two-dimensional domains. The assumptions in this paper are less restrictive than those considered so far in the literature allowing also variable coefficients, mixed derivatives and polygonal domains. The nonequidistant g...