Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems

Abstract : We consider the a posteriori error analysis of approximations of parabolic problems based on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high-order discontinuous Galerkin temporal discretizations. Using equilibrated flux reconstructions , we present a posteriori error estimates for a norm composed of the $L^2(H^1)\cap H^1(H^{-1})$-norm of the error and the temporal jumps of the numerical solution. The estimators provide guaranteed upper bounds for this norm, without unknown constants. Furthermore, the efficiency of the estimators with respect to this norm is local in both space and time, with constants that are robust with respect to the mesh-size, time-step size, and the spatial and temporal polynomial degrees. We further show that this norm, which is key for local space-time efficiency, is globally equivalent to the $L^2(H^1)\cap H^1(H^{-1})$-norm of the error, with polynomial-degree robust constants. The proposed estimators also have the practical advantage of allowing for very general refinement and coarsening between the timesteps.
Type de document :
Article dans une revue
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2017, 55 (6), pp.2811-2834. 〈http://epubs.siam.org/doi/abs/10.1137/16M1097626〉. 〈10.1137/16M1097626〉
Liste complète des métadonnées

Littérature citée [31 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01377086
Contributeur : Iain Smears <>
Soumis le : jeudi 6 octobre 2016 - 12:23:47
Dernière modification le : jeudi 26 avril 2018 - 10:28:49
Document(s) archivé(s) le : samedi 7 janvier 2017 - 13:01:21

Fichier

parabolic_aposteriori.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Alexandre Ern, Iain Smears, Martin Vohralík. Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2017, 55 (6), pp.2811-2834. 〈http://epubs.siam.org/doi/abs/10.1137/16M1097626〉. 〈10.1137/16M1097626〉. 〈hal-01377086〉

Partager

Métriques

Consultations de la notice

772

Téléchargements de fichiers

110