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Oscillation in a posteriori error estimation
Numerische Mathematik ( IF 2.1 ) Pub Date : 2021-04-09 , DOI: 10.1007/s00211-021-01194-8
Christian Kreuzer , Andreas Veeser

In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the following two properties. First, it is dominated by the error, irrespective of mesh fineness and the regularity of data and the exact solution. Second, it captures in terms of data the part of the residual that, in general, cannot be quantified with finite information. The new twist in our approach is a locally stable projection onto discretized residuals.



中文翻译:

后验误差估计中的振荡

在后验误差分析中,误差和估计量之间的关系通常被所谓的振荡项所破坏,而振荡项不能被误差所限制。为了补救,我们设计了一种新的方法,其中振荡具有以下两个属性。首先,无论网格的细度,数据的规则性和精确的解决方案如何,误差都将由误差决定。其次,它以数据的形式捕获通常无法用有限信息量化的残差部分。我们方法的新变化是离散离散残差上的局部稳定投影。

更新日期:2021-04-09
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