Ultraconvergence of the patch recovery technique II

Zhang, Zhimin

doi:10.1090/S0025-5718-99-01205-3

Ultraconvergence of the patch recovery technique II
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by Zhimin Zhang;

Math. Comp. 69 (2000), 141-158

DOI: https://doi.org/10.1090/S0025-5718-99-01205-3

Published electronically: August 25, 1999

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Abstract:

The ultraconvergence property of a gradient recovery technique proposed by Zienkiewicz and Zhu is analyzed for the Laplace equation in the two dimensional setting. Under the assumption that the pollution effect is not present or is properly controlled, it is shown that the convergence rate of the recovered gradient at an interior node is two orders higher than the optimal global convergence rate when even-order finite element spaces and local uniform rectangular meshes are used.

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