Efficient and reliable hierarchical error estimates for the discretization error of elliptic obstacle problems
Efficient and reliable hierarchical error estimates for the discretization error of elliptic obstacle problems
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DOI：
10.1090/s0025-5718-2010-02394-4
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
R. Kornhuber;Q. Zou
中科院分区：
文献类型：
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作者：
R. Kornhuber;Q. Zou
我们提出并分析了新的分层后验误差估计的自伴椭圆障碍问题。我们的方法不同于简单的，但不可靠的估计由一个额外的长期占离散自由边界的偏差在本地化步骤。我们证明了效率和可靠性的饱和假设和规则性条件下的底层网格。启发式的论点表明，额外的长期是更高的秩序，并保持充分的地方。数值计算证实了我们的理论发现。
We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the underlying grid. Heuristic arguments suggest that the extra term is of higher order and preserves full locality. Numerical computations confirm our theoretical findings.