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 Access content directly
Journal Articles Numerische Mathematik Year : 2022

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

Abstract

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
Origin Files produced by the author(s)

Dates and versions

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

Identifiers

Cite

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⟩
312 View
137 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More