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.
Oscillation in a posteriori error estimation / C. Kreuzer, A. Veeser. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 148:1(2021 May), pp. 43-78. [10.1007/s00211-021-01194-8]
Oscillation in a posteriori error estimation
A. Veeser
2021
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
Kreuzer-Veeser2021_Article_OscillationInAPosterioriErrorE.pdf
accesso aperto
Tipologia:
Publisher's version/PDF
Dimensione
549.13 kB
Formato
Adobe PDF
|
549.13 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.