Ultraconvergence of the patch recovery technique
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- by Zhimin Zhang PDF
- Math. Comp. 65 (1996), 1431-1437 Request permission
Abstract:
The ultraconvergence property of a derivative recovery technique recently proposed by Zienkiewicz and Zhu is analyzed for two-point boundary value problems. Under certain regularity assumptions on the exact solution, it is shown that the convergence rate of the recovered derivative at an internal nodal point is two orders higher than the optimal global convergence rate when even-order finite element spaces and local uniform meshes are used.References
- Barna Szabó and Ivo Babuška, Finite element analysis, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1991. MR 1164869
- L.B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics, Vol. 1605, Springer, Berlin, 1995
- O. C. Zienkiewicz and J. Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. I. The recovery technique, Internat. J. Numer. Methods Engrg. 33 (1992), no. 7, 1331–1364. MR 1161557, DOI 10.1002/nme.1620330702
Additional Information
- Zhimin Zhang
- Affiliation: Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
- MR Author ID: 303173
- Email: zhang@ttmath.ttu.edu
- Received by editor(s): June 22, 1995
- Received by editor(s) in revised form: November 2, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 1431-1437
- MSC (1991): Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-96-00782-X
- MathSciNet review: 1370858