Convergence of simple adaptive Galerkin schemes based on h-h/2 error estimators
Convergence of simple adaptive Galerkin schemes based on h-h/2 error estimators
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DOI：
10.1007/s00211-010-0292-9
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发表时间：
2010-08-01
影响因子：
2.1
通讯作者：
Praetorius, D.
中科院分区：
文献类型：
--
作者：
Ferraz-Leite, S.;Ortner, C.;Praetorius, D.
讨论了几种基于（h-h/2）-误差估计的自适应网格加密策略。这类自适应方法在实践中特别受欢迎，因为它是问题独立的，几乎不需要任何实现开销。我们证明了，在饱和假设下，这些自适应算法是收敛的。我们的框架不仅适用于有限元方法，但也产生了自适应边界元格式的第一个收敛性证明。对于一个有限元模型问题，我们扩展了所提出的自适应方案，并证明收敛性，即使饱和假设未能举行一般。
We discuss several adaptive mesh-refinement strategies based on (h - h/2)-error estimation. This class of adaptive methods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general.