✦ LIBER ✦

Mathematical analysis of Zienkiewicz—Zhu's derivative patch recovery technique

✍ Scribed by Zhimin Zhang

Book ID: 102657170
Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 764 KB
Volume: 12
Category: Article
ISSN: 0749-159X
DOI: 10.1002/(sici)1098-2426(199607)12:4<507::aid-num6>3.0.co;2-q

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✦ Synopsis

Zienkiewicz-Zhu's derivative patch recovery technique is analyzed for general quadrilateral finite elements. Under certain regular conditions on the meshes, the arithmetic mean of the absolute error of the recovered gradient at the nodal points is superconvergent for the second-order elliptic operators. For rectangular meshes and the Laplacian, the recovered gradient is superconvergent in the maximum norm at the nodal points. Furthermore, it is proved for a model two-point boundaryvalue problem that the recovery technique results in an "ultra-convergent" derivative recovery at the nodal points for quadratic finite elements when uniform meshes are used.

📜 SIMILAR VOLUMES

A robust implementation of Zienkiewicz a

A robust implementation of Zienkiewicz and Zhu's local patch recovery method

✍ Labbé, P. ;Garon, A 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 440 KB

Analysis of the superconvergent patch re

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

✍ Zhimin Zhang; J.Z. Zhu 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 856 KB

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