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

By Claire Chainais-Hillairet

Appears in 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).

Information about the video

Date of recording 01/05/2019
Date of publication 28/05/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19529003
Cite this video 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

Domain(s)

Bibliography

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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
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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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