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Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities

Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities
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Year:    2010

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 11–31

Abstract

For the linear finite element solution to the Poisson equation, we show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the $L^2$-projection from the piecewise constant field $∇u_N$ to the continuous and piecewise linear finite element space gives a better approximation of $∇u$ in the $H^1$-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.09-m1002

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 11–31

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Superconvergence Graded meshes Weighted Sobolev spaces Singular solutions The finite element method Gradient recovery schemes.

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