Hierarchical error estimates for the energy functional in obstacle problems
Hierarchical error estimates for the energy functional in obstacle problems
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DOI：
10.1007/s00211-011-0364-5
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发表时间：
2011-04
影响因子：
2.1
通讯作者：
Q. Zou;A. Veeser;R. Kornhuber;Carsten Gräser
中科院分区：
文献类型：
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作者：
Q. Zou;A. Veeser;R. Kornhuber;Carsten Gräser
我们提出了对称障碍问题中能量泛函最小值的分层后验误差分析。主要结果是，能量最小值的误差，直到振荡项，相当于适当的分层估计器。该证明没有引用任何饱和假设。我们甚至表明，小振荡意味着相关的饱和假设。此外，我们证明了离散化误差的后验估计的效率和可靠性，从而为以前的分层估计器的理论理解提供了一些启示。最后，我们通过数值计算说明了我们的理论结果。
We present a hierarchical a posteriori error analysis for the minimum value of the energy functional in symmetric obstacle problems. The main result is that the error in the energy minimum is, up to oscillation terms, equivalent to an appropriate hierarchical estimator. The proof does not invoke any saturation assumption. We even show that small oscillation implies a related saturation assumption. In addition, we prove efficiency and reliability of an a posteriori estimate of the discretization error and thereby cast some light on the theoretical understanding of previous hierarchical estimators. Finally, we illustrate our theoretical results by numerical computations.