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Entropy-Diminishing CVFE Scheme for Solving Anisotropic Degenerate Diffusion Equations

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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

Abstract

We consider a Control Volume Finite Elements (CVFE) scheme for solving possibly degenerated parabolic equations. This scheme does not require the introduction of the so-called Kirchhoff transform in its definition. The discrete solution obtained via the scheme remains in the physical range whatever the anisotropy of the problem, while the natural entropy of the problem decreases with time. Moreover, the discrete solution converges towards the unique weak solution of the continuous problem. Numerical results are provided and discussed.

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Acknowledgments

This work was supported by the French National Research Agency ANR (project GeoPor, grant ANR-13-JS01-0007-01).

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Sorbonne Universités, UPMC University Paris 06, UMR 7598, 75005, Paris, France

    Clément Cancès & Cindy Guichard

  2. Laboratoire Jacques-Louis Lions, CNRS, UMR 7598, 75005, Paris, France

    Clément Cancès & Cindy Guichard

Authors
  1. Clément Cancès
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  2. Cindy Guichard
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Corresponding author

Correspondence to Clément Cancès .

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Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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Cancès, C., Guichard, C. (2014). Entropy-Diminishing CVFE Scheme for Solving Anisotropic Degenerate Diffusion Equations. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_17

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