Long-time behaviour of hybrid finite volume ...
Document type :
Article dans une revue scientifique: Article original
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Title :
Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches
Author(s) :
Chainais-Hillairet, Claire [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Herda, Maxime [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Lemaire, Simon [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Moatti, Julien [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Reliable numerical approximations of dissipative systems [RAPSODI]
Herda, Maxime [Auteur]

Reliable numerical approximations of dissipative systems [RAPSODI]
Lemaire, Simon [Auteur]

Reliable numerical approximations of dissipative systems [RAPSODI]
Moatti, Julien [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Journal title :
Numerische Mathematik
Pages :
963-1016
Publisher :
Springer Verlag
Publication date :
2022
ISSN :
0029-599X
English keyword(s) :
Finite volume schemes
General meshes
Anisotropic advection-diffusion equations
Long-time behaviour
Entropy method
General meshes
Anisotropic advection-diffusion equations
Long-time behaviour
Entropy method
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [en]
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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
ANR Project :
Collections :
Source :
Submission date :
2025-01-24T15:56:47Z
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