Mathematics of Computation

Analysis of recovery type a posteriori error estimators for mildly structured grids

Author(s): Jinchao Xu; Zhimin Zhang.
Journal: Math. Comp. 73 (2004), 1139-1152.
MSC (2000): Primary 65N30; Secondary 65N50, 65N15, 65N12, 65D10, 74S05, 41A10, 41A25
Posted: August 19, 2003
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Abstract: Some recovery type error estimators for linear finite elements are analyzed under $O(h^{1+\alpha})$ $(\alpha > 0)$ regular grids. Superconvergence of order $O(h^{1+\rho})$ $(0 < \rho \le \alpha)$ is established for recovered gradients by three different methods. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.

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Jinchao Xu
Affiliation: Center for Computational Mathematics and Applications, Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: xu@math.psu.edu

Zhimin Zhang
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: zzhang@math.wayne.edu

DOI: 10.1090/S0025-5718-03-01600-4
PII: S 0025-5718(03)01600-4
Keywords: Gradient recovery, ZZ patch recovery, superconvergence, {\it a posteriori} error estimates
Received by editor(s): June 26, 2002
Received by editor(s) in revised form: December 15, 2002
Posted: August 19, 2003
Additional Notes: The work of the first author was supported in part by the National Science Foundation grant DMS-9706949 and the Center for Computational Mathematics and Applications, Penn State University
The work of the second author was supported in part by the National Science Foundation grants DMS-0074301, DMS-0079743, and INT-0196139
Copyright of article: Copyright 2003, American Mathematical Society

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