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Mathematics of Computation

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Ultraconvergence of the patch recovery technique

Author: Zhimin Zhang
Journal: Math. Comp. 65 (1996), 1431-1437
MSC (1991): Primary 65N30
MathSciNet review: 1370858
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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 [Enhancements On Off] (What's this?)

  • [1] Barna Szabó and Ivo Babuška, Finite element analysis, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1991. MR 1164869
  • [2] L.B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics, Vol. 1605, Springer, Berlin, 1995
  • [3] 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, 10.1002/nme.1620330702

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Additional Information

Zhimin Zhang
Affiliation: Department of Mathematics, Texas Tech University, Lubbock, Texas 79409

Received by editor(s): June 22, 1995
Received by editor(s) in revised form: November 2, 1995
Article copyright: © Copyright 1996 American Mathematical Society