Evaluation of some error estimators for the four‐noded lagrangian quadrilateral

Ramsay, A. C. A.; Sbresny, H.

doi:10.1002/cnm.1640110604

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Error estimation based on Superconvergent Patch Recovery using statically admissible stress fields

Kvamsdal

Okstad

1998

Int. J. Numer. Meth. Engng.

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In this paper we investigate an approach for a posteriori error estimation based on recovery of an improved stress ÿeld. The qualitative properties of the recovered stress ÿeld necessary to obtain a conservative error estimator, i.e. an upper bound on the true error, are given. A speciÿc procedure for recovery of an improved stress ÿeld is then developed. The procedure can be classiÿed as Superconvergent Patch Recovery (SPR) enhanced with approximate satisfaction of the interior equilibrium and the natural boundary conditions. Herein the interior equilibrium is satisÿed a priori within each nodal patch. Compared to the original SPR-method, which usually underestimates the true error, the present approach gives a more conservative estimate. The performance of the developed error estimator is illustrated by investigating two plane strain problems with known closed-form solutions. ? 1998 John Wiley & Sons, Ltd.

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