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Ultraconvergence of the patch recovery technique II
Author(s):
Zhimin
Zhang.
Journal:
Math. Comp.
69
(2000),
141-158.
MSC (1991):
Primary 65N30;
Secondary 65N15
Posted:
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.
References:
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- L.B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics, Vol. 1605, Springer, Berlin, 1995. MR 98j:65083
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- Z. Zhang, Ultraconvergence of the patch recovery technique, Math. Comp. 65 (1996), 1431-1437. MR 97a:65068
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- 8.
- O.C. Zienkiewicz and J.Z. Zhu, The superconvergence patch recovery and a posteriori error estimates. Part 1: The recovery technique, Internat. J. Numer. Meth. Eng. 33 (1992), 1331-1364.
- 9.
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Additional Information:
Zhimin
Zhang
Affiliation:
Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
Email:
zhang@ttmath.ttu.edu
DOI:
10.1090/S0025-5718-99-01205-3
PII:
S 0025-5718(99)01205-3
Received by editor(s):
August 7, 1996
Posted:
August 25, 1999
Additional Notes:
This work was supported in part under NSF Grants No. DMS-9626193, No. DMS-9622690 and No. INT-9605050.
Copyright of article:
Copyright
1999,
American Mathematical Society
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