Abstract
The shape of elements in the finite element analysis may be the most important of many factors which induce a discretizing error. In particular, the efficiency of adaptive refinement analysis depends on the shape of the elements, and so estimating the quality of element shape is requisite during the adaptive analysis being performed. Unfortunately, most posterior error estimates can not evaluate the shape error of an element, so that some difficulties remain in the application of an adaptive analysis. For this purpose, an error estimator which can separately evaluate size error and distortion error from Zienkiewicz-Zhu's error estimator is presented for bilinear and quadratic isoparametric finite elements. As deduced from the results of numerical experiments, the suggeted estimator gives a reasonable evaluation of error due to element shape as well as discretizing error.
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