The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
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DOI：
10.1002/nme.1620330703
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发表时间：
1992-05
影响因子：
2.9
通讯作者：
O. Zienkiewicz;J. Z. Zhu
中科院分区：
文献类型：
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作者：
O. Zienkiewicz;J. Z. Zhu
在本文的第二部分中，讨论了后验误差估计的问题。特别是，我们推导出一个定理，显示的Zienkiewicz-Zhu误差估计的收敛速度的有效性指标的依赖。这表明，与超收敛恢复的有效性指标趋于渐近统一。本文第一部分中提出的超收敛恢复技术用于Zienkiewicz-Zhu误差估计量的计算，以证明可达到的精确误差的精确估计。各种元素类型的数值试验示出的能量范数和逐点梯度（应力）误差估计的误差估计的优良有效性。文中还给出了误差估计器在自适应网格加密中的性能的几个例子。
In this second part of the paper, the issue of a posteriori error estimation is discussed. In particular, we derive a theorem showing the dependence of the effectivity index for the Zienkiewicz–Zhu error estimator on the convergence rate of the recovered solution. This shows that with superconvergent recovery the effectivity index tends asymptotically to unity. The superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the Zienkiewicz–Zhu error estimator to demonstrate accurate estimation of the exact error attainable. Numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient (stress) error estimation. Several examples of the performance of the error estimator in adaptive mesh refinement are also presented.