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A posteriori Error Control at Numerical Solution of Plate Bending Problem

机译：板弯题数值解的后验误差控制

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摘要

The classical approach to a posteriori error control considered in this paper bears on the counter variational principles of Lagrange and Castigliano. Its efficient implementation for problems of mechanics of solids assumes obtaining equilibrated stresses/resultants which, at the same time, are sufficiently close to the exact ones. Besides, it is important that computation of the error bound with the use of such stresses/resultants would be cheap in respect to the arithmetic work. Following these guide lines, we expand our preceding results for elliptic partial differential equations and theory elasticity equations upon the problem of thin plate bending. We derive guaranteed a posteriori error bounds of simple forms for solutions, obtained by the finite element method, and discuss algorithms of linear complexity for their computation. The approach of the paper also makes possible to improve some known general a posteriori estimates by means of arbitrary not equilibrated stress fields.
机译：本文中考虑了后验误差控制的经典方法，对拉格朗兰和Castigliano的反分区原理承担。其有效地实现固体力学问题假定在同时获得平衡的应力/结果，该结果是足够接近精确的应力/结果。此外，重要的是，在使用这种应力/结果的情况下，对算术工作的使用来计算误差。遵循这些导向线，我们在薄板弯曲问题上扩展了椭圆局部微分方程和理论弹性方程的前面的结果。通过有限元方法获得的解决方案的简单表单的后验误差界，并讨论了它们计算的线性复杂性的算法。本文的方法还可以通过任意不平衡的应力场来改善一些已知的一般估计。

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