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The superconvergent patch recovery and $a\ posteriori$ error estimates. II: Error estimates and adaptivity. (English) Zbl 0769.73085
Summary: 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 [see the foregoing entry] is 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.

##### MSC:
 74S05 Finite element methods in solid mechanics 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) 65N15 Error bounds (BVP of PDE)
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