Nonlinear free energy diminishing schemes for convection-diffusion equations: convergence and long time behaviour | Vidéo | Carmin.tv

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Nonlinear free energy diminishing schemes for convection-diffusion equations: convergence and long time behaviour

De Claire Chainais-Hillairet

Apparaît dans la collection : POEMs - POlytopal Element Methods in Mathematics and Engineering

The aim of the talk is to introduce a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift-diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation relation. This relation is of paramount importance to capture the long-time behavior of the problem in an accurate way. To enforce it, the linear convection diffusion equation is rewritten in a nonlinear form before being discretized. This is a joint work with Clément Cancès (Lille) and Stella Krell (Nice).

Informations sur la vidéo

Date de captation 01/05/2019
Date de publication 28/05/2019
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19529003
Citer cette vidéo Chainais-Hillairet, Claire (01/05/2019). Nonlinear free energy diminishing schemes for convection-diffusion equations: convergence and long time behaviour. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19529003
URL https://dx.doi.org/10.24350/CIRM.V.19529003

Domaine(s)

Bibliographie

CHAINAIS-HILLAIRET, Claire et HERDA, Maxime. Large-time behavior of a family of finite volume schemes for boundary-driven convection-diffusion equations. arXiv preprint arXiv:1810.01087, 2018. - https://arxiv.org/abs/1810.01087
BURMAN, Erik et ERN, Alexandre. Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes. Comptes Rendus Mathematique, 2004, vol. 338, no 8, p. 641-646. - https://doi.org/10.1016/j.crma.2004.02.010
CANCÈS, Clément, CATHALA, Mathieu, et LE POTIER, Christophe. Monotone corrections for generic cell-centered finite volume approximations of anisotropic diffusion equations. Numerische Mathematik, 2013, vol. 125, no 3, p. 387-417. - https://doi.org/10.1007/s00211-013-0545-5ISTEX
CANCÈS, Clément et GUICHARD, Cindy. Convergence of a nonlinear entropy diminishing control volume finite element scheme for solving anisotropic degenerate parabolic equations. Mathematics of Computation, 2016, vol. 85, no 298, p. 549-580. - https://hal.archives-ouvertes.fr/hal-00955091
DOMELEVO, Komla et OMNES, Pascal. A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids. ESAIM: Mathematical Modelling and Numerical Analysis, 2005, vol. 39, no 6, p. 1203-1249. - https://doi.org/10.1051/m2an:2005047
COUDIÈRE, Yves, VILA, Jean-Paul, et VILLEDIEU, Philippe. Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem. ESAIM: Mathematical Modelling and Numerical Analysis, 1999, vol. 33, no 3, p. 493-516. - [https://doi.org/10.1051/m2an:1999149 I](https://doi.org/10.1051/m2an:1999149 I)
ANDREIANOV, Boris, BOYER, Franck, et HUBERT, Florence. Discrete duality finite volume schemes for leray− lions− type elliptic problems on general 2D meshes. Numerical Methods for Partial Differential Equations: An International Journal, 2007, vol. 23, no 1, p. 145-195. - https://doi.org/10.1002/num.20170ISTEX
ANDREIANOV, Boris, BENDAHMANE, Mostafa, et KARLSEN, Kenneth Hvistendahl. Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations. Journal of Hyperbolic Differential Equations, 2010, vol. 7, no 01, p. 1-67. - https://arxiv.org/abs/0901.0816
CANCÈS, Clément, CHAINAIS-HILLAIRET, Claire, et KRELL, Stella. Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations. Computational Methods in Applied Mathematics, 2018, vol. 18, no 3, p. 407-432. - https://arxiv.org/abs/1705.10558

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