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

Mingxia Li, Shipeng Mao

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Superconvergence, Mathematics, Bilinear interpolation, Finite element method, Polygon mesh, Bilinear form, Applied mathematics, Mathematical analysis

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