The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

被引：21
作者：
Cifani, Simone [1 ]
Jakobsen, Espen R. [1 ]
Karlsen, Kenneth H. [2 ]
机构：
[1] Norwegian Univ Sci & Technol NTNU, Dept Math, N-7491 Trondheim, Norway
[2] Univ Oslo, Dept Math, Ctr Math Applicat CMA, N-0316 Oslo, Norway
来源：
BIT NUMERICAL MATHEMATICS | 2011年 / 51卷 / 04期
关键词：
Convection-diffusion equations; Degenerate parabolic; Conservation laws; Fractional diffusion; Entropy solutions; Direct/local discontinuous Galerkin methods; APPROXIMATION;
D O I：
10.1007/s10543-011-0327-3
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L,vy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments.
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页码：809 / 844
页数：36
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