The highest order superconvergence for bi-𝑘 degree rectangular elements at nodes: A proof of 2𝑘-conjecture

Chen, Chuanmiao; Hu, Shufang

doi:10.1090/S0025-5718-2012-02653-6

The highest order superconvergence for bi- degree rectangular elements at nodes: A proof of -conjecture

Authors: Chuanmiao Chen and Shufang Hu
Journal: Math. Comp. 82 (2013), 1337-1355
MSC (2010): Primary 65N30, 65N15
DOI: https://doi.org/10.1090/S0025-5718-2012-02653-6
Published electronically: December 5, 2012
MathSciNet review: 3042566
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Abstract: We proved the highest order superconvergence $(u-u_h)(z)=O(h^{2k})\vert\ln h\vert$ at nodes , based on Element Orthogonality Analysis (EOA), correction techniques and tensor product, where $u\in W^{2k,\infty }(\Omega )$ is the solution for the Poisson equation $-\Delta u=f$ in a rectangle $\Omega$ , on $\Gamma$ , and $u_h\in S^h_0$ is its bi- degree rectangular finite element approximation. This conclusion is also verified by numerical experiments for .

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