Localization of the $W^{-1,q}$ norm for local a posteriori efficiencyReport as inadecuate

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* Corresponding author 1 CZ-KARLMP-MI - Mathematical Institute 2 SERENA - Simulation for the Environment : Reliable and Efficient Numerical Algorithms Inria Paris-Rocquencourt

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.

Keywords : a posteriori error estimate finite element method nonlinear partial differential equation residual Sobolev space W^{1p} 0Ω functional dual norm local structure

Author: Jan Blechta - Josef Málek - Martin Vohralík -

Source: https://hal.archives-ouvertes.fr/


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