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BASIC STRUCTURES OF SUPER CONVERGENCE IN FINITE ELEMENT ANALYSIS

Chuanmiao Chen

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Abstract

Superconvergence for second order elliptic finite elements on uniform meshes is discussed. The element orthogonality analysis method and the orthogonality correction technique are especially emphasized. There are two basic structures of superconvergence, i.e. Gauss-Lobatto points and symmetric points. Their accuracy and global property are also analysed. Four main principles in using superconvergence are proposed.

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What this paper is about

Superconvergence for second order elliptic finite elements on uniform meshes is discussed. The element orthogonality analysis method and the orthogonality correction technique are especially emphasized. There are two basic structures of superconvergence, i.e. Gauss-Lobatto points and symmetric points. Their accuracy and global property are also analysed. Four main principles in using superconvergence are proposed.

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Available abstract

Superconvergence for second order elliptic finite elements on uniform meshes is discussed. The element orthogonality analysis method and the orthogonality correction technique are especially emphasized. There are two basic structures of superconvergence, i.e. Gauss-Lobatto points and symmetric points. Their accuracy and global property are also analysed. Four main principles in using superconvergence are proposed.

Key concepts: Superconvergence, Orthogonality, Mathematics, Finite element method, Convergence (economics), Gauss, Mathematical analysis, Polygon mesh

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