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H 1 Nonlinear free energy diminishing schemes for convection-diffusion equations: convergence and long time behaviour

Auteurs : Chainais-Hillairet, Claire (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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).

    Codes MSC :
    65M12 - Stability and convergence of numerical methods (IVP of PDE)
    65M08 - Finite volume methods

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 28/05/2019
      Date de captation : 01/05/2019
      Collection : Research talks
      Format : MP4
      Durée : 00:42:08
      Domaine : PDE ; Numerical Analysis & Scientific Computing
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-05-01_Chainais.mp4

    Informations sur la rencontre

    Nom de la rencontre : POEMs - POlytopal Element Methods in Mathematics and Engineering
    Organisateurs de la rencontre : Antonietti, Paola ; Beirão da Veiga, Lourenço ; Di Pietro, Daniele ; Droniou, Jérôme ; Krell, Stella
    Dates : 29/04/2019 - 03/05/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/1954.html

    Citation Data

    DOI : 10.24350/CIRM.V.19529003
    Cite this video as: Chainais-Hillairet, Claire (2019). Nonlinear free energy diminishing schemes for convection-diffusion equations: convergence and long time behaviour. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19529003
    URI : http://dx.doi.org/10.24350/CIRM.V.19529003


    Voir aussi

    Bibliographie

    1. 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

    2. 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

    3. 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

    4. 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

    5. 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

    6. 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

    7. 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

    8. 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

    9. 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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