Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Numerische Mathematik Année : 2022

Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches

Résumé

We are interested in the long-time behaviour of approximate solutions to anisotropic and heterogeneous linear advection-diffusion equations in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. We consider two linear methods, as well as a new, nonlinear scheme, for which we prove the existence and the positivity of discrete solutions. We show that the discrete solutions to the three schemes converge exponentially fast in time towards the associated discrete steady-states. To illustrate our theoretical findings, we present some numerical simulations assessing long-time behaviour and positivity. We also compare the accuracy of the schemes on some numerical tests in the stationary case.
Fichier principal
Vignette du fichier
HFV_longtime(hal).pdf (581 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03281500 , version 1 (08-07-2021)
hal-03281500 , version 2 (28-02-2022)

Identifiants

Citer

Claire Chainais-Hillairet, Maxime Herda, Simon Lemaire, Julien Moatti. Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches. Numerische Mathematik, 2022, 151 (4), pp.963-1016. ⟨10.1007/s00211-022-01289-w⟩. ⟨hal-03281500v2⟩
301 Consultations
134 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More