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Polynomial Preserving Gradient Recovery and a Posteriori Estimate for Bilinear Element on Irregular Quadrilaterals

Polynomial Preserving Gradient Recovery and a Posteriori Estimate for Bilinear Element on Irregular Quadrilaterals
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Year:    2004

Author:    Zhimin Zhang

International Journal of Numerical Analysis and Modeling, Vol. 1 (2004), Iss. 1 : pp. 1–24

Abstract

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under quadrilateral meshes. It has been proven that the recovered gradient converges at a rate $O(h^{1+\rho})$ for $\rho = min(\alpha, 1)$, when the mesh is distorted $O(h^{1+\alpha})$ ($\alpha > 0$) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ijnam.OA-2004-1101

International Journal of Numerical Analysis and Modeling, Vol. 1 (2004), Iss. 1 : pp. 1–24

Published online:    2004-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Finite element method quadrilateral mesh gradient recovery superconvergence a posteriori error estimate.

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