# Localization of the $W^{-1,q}$ norm for local a posteriori efficiency

Abstract : This paper gives a direct proof of localization of dual norms of bounded linear functionals on the Sobolev space $W^{1,p}_0(\Omega)$. The basic condition is that the functional in question vanishes over locally supported test functions from $W^{1,p}_0(\Omega)$ which form a partition of unity in $\Omega$, apart from close to the boundary $\partial \Omega$. We also study how to weaken this condition. The results allow in particular to establish local efficiency and robustness of a posteriori estimates for nonlinear partial differential equations in divergence form, including the case of inexact solvers.
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Type de document :
Pré-publication, Document de travail
2016

https://hal.inria.fr/hal-01332481
Contributeur : Martin Vohralik <>
Soumis le : dimanche 15 janvier 2017 - 22:08:10
Dernière modification le : lundi 30 janvier 2017 - 11:18:59

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norms_nonlin.pdf
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• HAL Id : hal-01332481, version 2

### Citation

Jan Blechta, Josef Málek, Martin Vohralík. Localization of the $W^{-1,q}$ norm for local a posteriori efficiency. 2016. <hal-01332481v2>

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