Basic structures of superconvergence in finite element analysis. (English) Zbl 1066.65112

Chan, Tony F. (ed.) et al., Recent progress in computational and applied PDEs. Conference proceedings for the international conference held in Zhangjiajie, China, July 1–7, 2001. New York, NY: Kluwer Academic / Plenum Publishers (ISBN 0-306-47420-4/hbk). 113-122 (2002).
Summary: 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.
For the entire collection see [Zbl 1053.65001].


65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations