Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error
Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error
复制标题
平衡补丁恢复误差估计：简单而准确的误差上限
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
O. Zienkiewicz
中科院分区：
文献类型：
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作者：
P. Díez;Juan José Ródenas;O. Zienkiewicz
本文介绍了一种新的恢复型误差估计，确保局部平衡，并产生一个有保证的误差上界。上限性质要求恢复的解决方案是静态平衡和连续的。平衡是局部获得的（逐块），连续性是通过基于单位概念划分的后处理来实现的。这种后处理有望保留局部平衡应力场的特征。然而，后处理阶段修改了平衡，不再完全满足。一个新的方法，产量上限估计考虑到这种缺乏平衡。这需要计算误差的范数，或将其与能量范数相关联。
This paper introduces a new recovery‐type error estimator ensuring local equilibrium and yielding a guaranteed upper bound of the error. The upper bound property requires the recovered solution to be both statically equilibrated and continuous. The equilibrium is obtained locally (patch‐by‐patch) and the continuity is enforced by a postprocessing based on the partition of the unity concept. This postprocess is expected to preserve the features of the locally equilibrated stress field. Nevertheless, the postprocess phase modifies the equilibrium, which is no longer exactly fulfilled. A new methodology is introduced that yields upper bound estimates by taking into account this lack of equilibrium. This requires computing the ℒ︁2 norm of the error or relating it with the energy norm.