Discrete $p$-robust Hdiv-liftings and a posteriori estimates for elliptic problems with $H^{-1}$ source termsReportar como inadecuado

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1 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique 2 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms Inria de Paris

Abstract : We establish the existence of liftings into discrete subspaces of Hdiv of piecewise polynomial data on locally refined simplicial partitions of polygonal-polyhedral domains. Our liftings are robust with respect to the polynomial degree. This result has important applications in the a posteriori error analysis of parabolic problems, where it permits the removal of so-called transition conditions that link two consecutive meshes. It can also be used in a the posteriori error analysis of elliptic problems, where it allows the treatment of meshes with arbitrary numbers of hanging nodes between elements. We present a constructive proof based on the a posteriori error analysis of an auxiliary elliptic problem with $H^{−1}$ source terms, thereby yielding results of independent interest. In particular, for such problems, we obtain guaranteed upper bounds on the error along with polynomial-degree robust local efficiency of the estimators.

Keywords : Hdiv liftings right-inverse of divergence a posteriori error analysis polynomial degree robustness stability of mixed methods

Autor: Alexandre Ern - Iain Smears - Martin Vohralík -

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


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