Entropy-Diminishing CVFE Scheme for Solving Anisotropic Degenerate Diffusion Equations

  • Clément Cancès
  • Cindy Guichard
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 77)


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.


Dirichlet Boundary Condition Continuous Problem Discrete Solution Permeability Tensor Degenerate Parabolic Equation 
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This work was supported by the French National Research Agency ANR (project GeoPor, grant ANR-13-JS01-0007-01).


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis LionsSorbonne Universités, UPMC University Paris 06, UMR 7598ParisFrance
  2. 2.Laboratoire Jacques-Louis LionsCNRS, UMR 7598ParisFrance

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