Guaranteed and robust error bounds for nonconforming approximations of elliptic problems
Guaranteed and robust error bounds for nonconforming approximations of elliptic problems
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DOI：
10.1093/imanum/drp037
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发表时间：
2011-04
影响因子：
2.1
通讯作者：
S. Repin;S. Tomar
中科院分区：
文献类型：
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作者：
S. Repin;S. Tomar
我们提出了保证，鲁棒的和可计算的后验误差估计的椭圆问题的逼近。我们的分析是基于一个亥姆霍兹型分解的通量表示的错误。这样的分解导致一个梯度项和一个无发散项，这是两个辅助问题的精确解。我们提出了一种新的方法来获得这些解决方案的规范可计算的双边界。本文中获得的后验估计不同于那些基于投影的一致空间的逼近。数值实验证实，这些新的估计提供了非常准确的误差界，并可以有效地利用在实际计算中。
We present guaranteed, robust and computable a posteriori error estimates for nonconforming approximations of elliptic problems. Our analysis is based on a Helmholtz-type decomposition of the error expressed in terms of fluxes. Such a decomposition results in a gradient term and a divergence-free term, that are the exact solutions of two auxiliary problems. We suggest a new approach to deriving computable two-sided bounds of the norms of these solutions. The a posteriori estimates obtained in this paper differ from those that are based on projections of nonconforming approximations to a conforming space. Numerical experiments confirm that these new estimates provide very accurate error bounds, and can be efficiently exploited in practical computations.