Convergence of a nonlinear entropy diminishing Control Volume Finite Element scheme for solving anisotropic degenerate parabolic equations

Cancès, Clément; Guichard, Cindy

doi:10.1090/mcom/2997

Convergence of a nonlinear entropy diminishing Control Volume Finite Element scheme for solving anisotropic degenerate parabolic equations
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by Clément Cancès and Cindy Guichard PDF

Math. Comp. 85 (2016), 549-580 Request permission

Abstract:

In this paper, we propose and analyze 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. We prove that the discrete solution obtained via the scheme remains in the physical range, and that the natural entropy of the problem decreases with time. The convergence of the method is proved as the discretization steps tend to $0$. Finally, numerical examples illustrate the efficiency of the method.

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