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Analysis of the superconvergent patch recovery technique and a posteriori error estimator in the finite element method (II)

✍ Scribed by Zhimin Zhang; J.Z. Zhu

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 856 KB
Volume: 163
Category: Article
ISSN: 0045-7825
DOI: 10.1016/s0045-7825(98)00010-3

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✦ Synopsis

This is the second in a series of two papers in which the patch recovery technique proposed by Zienkiewicz and Zhu [I-3] is analyzed. In the first paper [4], we have shown that the recovered derivative by the least-squares titting is superconvergent for the two-point boundary value problems. In the present work, we consider the two-dimensional case in which the tensor product elements are used. We show that the patch recovery technique yields superconvergence recovery for the gradient in both the L,-norm and the L,-norm. Consequently, the error estimator based on the recovered gradient is asymptotically exact.

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