Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada Année : 2024

Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity

J. Droniou
C. Guichard

Résumé

We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in space; the latter is in fact a class of methods that includes conforming and nonconforming finite elements, discontinuous Galerkin methods and several others. The main result is an error estimate which holds without supplementary regularity hypothesis on the solution. This result states that the approximation error has the same order as the sum of the interpolation error and the conformity error. The proof of this result relies on an inf-sup inequality in Hilbert spaces which can be used both in the continuous and the discrete frameworks. The error estimate result is illustrated by numerical examples with low regularity of the solution.
Fichier principal
Vignette du fichier
ester_gd_hal.pdf (588.71 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04183945 , version 1 (21-08-2023)

Licence

Paternité

Identifiants

Citer

J. Droniou, R. Eymard, T. Gallouët, C. Guichard, R. Herbin. Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity. SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, 2024, ⟨10.1007/s40324-024-00360-w⟩. ⟨hal-04183945⟩
55 Consultations
23 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More