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The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
Author(s) -
Zienkiewicz O. C.,
Zhu J. Z.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330703
Subject(s) - superconvergence , estimator , pointwise , a priori and a posteriori , mathematics , rate of convergence , norm (philosophy) , computation , convergence (economics) , finite element method , mathematical optimization , statistics , computer science , algorithm , mathematical analysis , philosophy , epistemology , political science , law , economics , economic growth , computer network , physics , channel (broadcasting) , thermodynamics
In this second part of the paper, the issue of a posteriori error estimation is discussed. In particular, we derive a theorem showing the dependence of the effectivity index for the Zienkiewicz–Zhu error estimator on the convergence rate of the recovered solution. This shows that with superconvergent recovery the effectivity index tends asymptotically to unity. The superconvergent recovery technique developed in the first part of the paper 1 is the used in the computation of the Zienkiewicz–Zhu error estimator to demonstrate accurate estimation of the exact error attainable. Numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient (stress) error estimation. Several examples of the performance of the error estimator in adaptive mesh refinement are also presented.