On adaptive computational methods: global norms controlling local errors
On adaptive computational methods: global norms controlling local errors
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自适应计算方法：控制局部误差的全局规范
DOI：
10.1515/156939506777443031
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发表时间：
2006
影响因子：
2
通讯作者：
F. Suttmeier
中科院分区：
文献类型：
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作者：
F. Suttmeier
在本文中，我们继续研究使用全局范数估计进行局部误差控制的有限元(FE)方法的优化网格设计。这些策略基于用于FE方案(例如参见[3，7，18])的后验差错控制的所谓的双重加权残差(DWR)方法，其中通过解决辅助(对偶)问题来建立对原始问题的差错控制。在这种情况下，我们指责(参见[17，18])全球标准估计在应用中不是那么有用。但是仔细观察DWR概念，可以观察到实际上可以使用全局误差界来建立局部差错控制。我们得到了严格的误差界，特别是我们控制了进入所提出估计的(未知)对偶解的逼近过程。此外，这些估计还提供了优化原始问题和对偶问题的近似过程的信息。
In this note, we continue our studies on optimised mesh design for the Finite Element (FE) method 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., [3,7,18]), where error control for the primal problem is established by solving an auxiliary (dual) problem. In this context we blamed (cf. [17,18]) global norm estimates being not that useful in applications. But having a closer look at the DWR-concept, one observes that in fact global error bounds can be employed to establish local error control. We derive rigorous error bounds, especially we control the approximation process of the (unknown) dual solution entering the proposed estimate. Additional, these estimates provide information to optimise the approximation process of the primal and dual problem.