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 $W^{1,p}_0(\Omega)$, $1 \leq p \leq \infty$. 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 with respect to the exponent $p$ of a posteriori estimates for nonlinear partial differential equations in divergence form, including the case of inexact solvers. Numerical illustrations support the theory.
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Pré-publication, Document de travail
2018
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https://hal.inria.fr/hal-01332481
Contributeur : Martin Vohralik <>
Soumis le : mercredi 4 juillet 2018 - 17:39:50
Dernière modification le : mardi 16 octobre 2018 - 12:45:06

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  • HAL Id : hal-01332481, version 3

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Jan Blechta, Josef Málek, Martin Vohralík. Localization of the $W^{-1,q}$ norm for local a posteriori efficiency. 2018. 〈hal-01332481v3〉

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