Entropy-diminishing CVFE scheme for solving anisotropic degenerate diffusion equations

Clément Cancès (1) , Cindy Guichard (1)

1 LJLL - Laboratoire Jacques-Louis Lions

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 weak solution of the continuous problem. Numerical results are provided and discussed.

Domaines: Analyse numérique [math.NA]

Clément Cancès, Cindy Guichard. Entropy-diminishing CVFE scheme for solving anisotropic degenerate diffusion equations. 2014. ⟨hal-00937595⟩