On computational methods for variational inequalities
On computational methods for variational inequalities
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变分不等式的计算方法
DOI：
10.1007/s00466-004-0628-3
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发表时间：
2005
影响因子：
4.1
通讯作者：
F. Suttmeier
中科院分区：
文献类型：
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作者：
F. Suttmeier
在这篇文章中，我们重点讨论了用全局范数估计进行局部误差控制的变分不等式有限元方法的优化网格设计。这些策略基于所谓的双加权残差（DWR）方法，用于fe方案的后验误差控制（参见，例如，Rannacher等人[19,6,2]），其中通过解决辅助（对偶）问题来建立原始问题的误差控制。在这种情况下，我们指责（例如，Rannacher和Suttmeier[18,19]）全局规范估计在应用程序中没有那么有用。但是如果仔细研究dwr概念，就会发现实际上可以利用全局（能量）误差界限来建立局部误差控制。我们的想法和技术在所谓的障碍问题中得到说明。结果表明，可靠和有效的能量误差控制是建立有用的局部量后验误差界的一个重要因素。此外，我们还导出了第一类椭圆型变分不等式能量范数的后验误差控制的统一方法。最后，这个框架被应用于西格里尼的问题。
In this note, we focus on optimised mesh design for the Finite Element (FE) method for variational inequalities using global norm estimates for local error control. The strategies are based on the so called dual-weighted-residual (DWR) approach to a posteriori error control for FE-schemes (see, e.g., Rannacher et al. [19, 6, 2]), where error control for the primal problem is established by solving an auxiliary (dual) problem. In this context we blamed (cf. e.g., Rannacher and Suttmeier [18, 19]) global norm estimates being not that useful in applications. But having a closer look at the DWR-concept, one observes that in fact global (energy) error bounds can be employed to establish local error control. Our ideas and techniques are illustrated at the socalled obstacle problem.It turns out, that reliable and efficient energy error control is one main ingredient to establish useful a posteriori error bounds for local quantities. Therefore, in addition, we derive an unified approach to a posteriori error control in the energy norm for elliptic variational inequalities of first kind. Eventually, this framework is applied to Signorini’s problem.