An arbitrary-order fully discrete Stokes complex on general polyhedral meshes - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue (Article De Synthèse) Mathematics of Computation Année : 2023

An arbitrary-order fully discrete Stokes complex on general polyhedral meshes

Résumé

In this paper we present an arbitrary-order fully discrete Stokes complex on general polyhedral meshes. We enriche the fully discrete de Rham complex with the addition of a full gradient operator defined on vector fields and fitting into the complex. We show a complete set of results on the novelties of this complex: exactness properties, uniform Poincaré inequalities and primal and adjoint consistency. The Stokes complex is especially well suited for problem involving Jacobian, divergence and curl, like the Stokes problem or magnetohydrodynamic systems. The framework developed here eases the design and analysis of scheme for such problems. Schemes built that way are nonconforming and benefit from the exactness of the complex. We illustrate with the design and study of a scheme to solve the Stokes equations and validate the convergence rates with various numerical tests.
Fichier principal
Vignette du fichier
Stokes.pdf (3.65 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03665576 , version 1 (11-05-2022)

Identifiants

Citer

Marien-Lorenzo Hanot. An arbitrary-order fully discrete Stokes complex on general polyhedral meshes. Mathematics of Computation, 2023, 92 (343), pp.1977-2023. ⟨10.1090/mcom/3837⟩. ⟨hal-03665576⟩
7 Consultations
9 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More