面向目标的自适应有限元法的平面收敛性

Valentin Helml, M. Innerberger, D. Praetorius
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引用次数: 0

摘要

针对不同的一般标记策略,我们在一致性有限元方法的框架下讨论了目标导向的自适应性和相关后检误差估计的平实收敛性。我们对两种不同的设置进行了抽象分析。首先,我们考虑局部离散效率估计成立的问题。其次,我们展示了在仅依赖于误差估计器的结构特性的情况下的简单收敛性,即在非精化元素上的稳定性以及在精化元素上的约简性。特别是,第二种设置不需要可靠性和效率估计。数值实验证实了我们的理论发现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Plain convergence of goal-oriented adaptive FEM
We discuss goal-oriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general marking strategies. We present an abstract analysis for two different settings. First, we consider problems where a local discrete efficiency estimate holds. Second, we show plain convergence in a setting that relies only on structural properties of the error estimators, namely stability on non-refined elements as well as reduction on refined elements. In particular, the second setting does not require reliability and efficiency estimates. Numerical experiments underline our theoretical findings.
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