ON THE SUPERCONVERGENCE OF BILINEAR FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS WITH GENERAL BOUNDARY CONDITIONS

Abstract. In this paper, the superconvergence of bilinear finite element for general second order elliptic problems with general boundary conditions is stud-ied to avoid a sub-optimal superconvergence, we construct an auxiliary equation to eliminate the effect of boundary terms. As a result, the O(h2) superconver-gence rate is obtained under the regularity assumption that u ∈ H3(Ω) when almost uniform rectangular meshes is employed, which improves the previous results