CONVERGENCE OF A NONLINEAR ENTROPY DIMINISHING CONTROL VOLUME FINITE ELEMENT SCHEME FOR SOLVING ANISOTROPIC DEGENERATE PARABOLIC EQUATIONS

被引：42

作者：

Cances, Clement ^{[1
,2
]}

Guichard, Cindy ^{[1
,2
,3
,4
]}

机构：

[1] Univ Paris 06, Sorbonne Univ, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France

[2] CNRS, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France

[3] Inria, ANGE Project Team, Rocquencourt BP 105, F-78153 Le Chesnay, France

[4] CEREMA, ANGE Project Team, 134 Rue Beauvais, F-60280 Margny Les Compiegne, France

来源：

MATHEMATICS OF COMPUTATION | 2016年 / 85卷 / 298期

关键词：

APPROXIMATE SOLUTIONS; 2-PHASE FLOWS;

D O I：

10.1090/mcom/2997

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：549 / 580

页数：32

共 44 条

[1] An optimal Poincare inequality in L1 for convex domains [J].