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

Abstract : This paper shows how to localize inside of a domain Ω dual norms of bounded linear functionals on the Sobolev space W^{1,p}_0(Ω). The only condition is that the functional in question vanishes over locally supported test functions from W^{1,p}_0(Ω) which form a partition of unity in Ω, apart from close to the boundary ∂Ω. The results allow in particular to establish local efficiency and robustness for a posteriori analysis of nonlinear partial differential equations in divergence form.
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https://hal.inria.fr/hal-01332481
Contributor : Martin Vohralik <>
Submitted on : Thursday, June 16, 2016 - 3:04:40 AM
Last modification on : Friday, May 25, 2018 - 12:02:07 PM

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norms_nonlin.pdf
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• HAL Id : hal-01332481, version 1

### Citation

Jan Blechta, Josef Málek, Martin Vohralík. Localization of the $W^{-1,q}$ norm for local a posteriori efficiency. 2016. ⟨hal-01332481v1⟩

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