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

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 methods on general polygonal/polyhedral meshes. We consider two linear methods, as well as a new, nonlinear scheme, for...

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Bibliographic Details
Published in:Numerische Mathematik 2022, Vol.151 (4), p.963-1016
Main Authors: Chainais-Hillairet, Claire, Herda, Maxime, Lemaire, Simon, Moatti, Julien
Format: Article
Language:English
Subjects:
Advection
Advection-diffusion equation
Finite volume method
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
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Summary: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 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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-022-01289-w