Abstract
In this paper, the properties of various boundary integral operators are investigated for error estimation in adaptive BEM. It is found that the residual of the hyper-singular boundary integral equation (BIE) can be used for a-posteriori error estimation for different kinds of problems. Based on this result, a new a-posteriori error indicator is proposed which is a measure of the difference of two solutions for boundary stresses in elastic BEM. The first solution is obtained by the conventional boundary stress calculation method, and the second one by use of the regularized hyper-singular BIE for displacement derivative. The latter solution has recently been found to be of high accuracy and can be easily obtained under the most commonly used C 0 continuous elements. This new error indicator is defined by a L 1 norm of the difference between the two solutions under Mises stress sense. Two typical numerical examples have been performed for two-dimensional (2D) elasticity problems and the results show that the proposed error indicator successfully tracks the real numerical errors and effectively leads a h-type mesh refinement procedure.
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Received: 8 May 2002 / Accepted: 10 December 2002
The financial support by the Alexander von Humboldt Foundation 10102019 and the Chinese Natural Science Foundation and Returning Scholar Foundation is gratefully acknowledged. The second author was supported by the Special Funds for State Major Basic Research Projects of China (G19990328). Thanks to Professors G.C. Hsiao and W.L. Wendland, and Doctors H. Andrä, H. Schulz, O. Steinbach and P. Lu for their helpful discussions while writing this paper.
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Chen, H., Yu, D. & Schnack, E. A simple a-posteriori error estimation for adaptive BEM in elasticity. Computational Mechanics 30, 343–354 (2003). https://doi.org/10.1007/s00466-003-0409-4
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DOI: https://doi.org/10.1007/s00466-003-0409-4