期刊论文详细信息
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 卷:265
On the superconvergence patch recovery techniques for the linear finite element approximation on anisotropic meshes
Article
Cao, Weiming
关键词: A-posteriori error estimate;    Superconvergence patch recovery;    Anisotropic mesh;    Linear finite element;    Post-processing;   
DOI  :  10.1016/j.cam.2013.09.031
来源: Elsevier
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【 摘 要 】

We provide in this paper an analysis on the superconvergence patch recovery (SPR) techniques for the linear finite element approximation based on adaptively refined anisotropic meshes in two dimensions. These techniques include the gradient recovery based on local weighted averaging, the recovery based on local L-2-projection, and the recovery based on least square fitting. The last one leads to the Zienkiewicz Zhu type error estimators popular in engineering communities. Based on the superconvergence result for anisotropic meshes established recently in Cao (2013), we prove that all three types of SPR techniques produce super-linearly convergent gradients if the meshes are quasi-uniform under a given metric and each pair of adjacent elements in the meshes form an approximate parallelogram. As a consequence, the error estimators based on the recovered gradient are asymptotically exact. These results provide a theoretical justification for the extraordinary robustness and accuracy observed in numerous applications for the recovery type error estimators on anisotropic meshes. (c) 2013 Elsevier B.V. All rights reserved.

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