Discrete negative norms in the analysis of supraconvergent two dimensional cell-centered schemes

Abstract

In this paper we study the convergence properties of cell-centered finite difference schemes for second order elliptic equations with variable coefficients. We prove that the finite difference schemes on nonuniform meshes although not even being consistent are nevertheless second order convergent. The convergence is studied with the aid of an appropriate negative norm. Numerical examples support the convergence result.