The discontinuous Galerkin method for fractal conservation laws

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 Sci, N-7491 Trondheim, Norway
[2] Univ Oslo, Dept Math, CMA, N-0316 Oslo, Norway
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2011年 / 31卷 / 03期
关键词：
fractal; fractional conservation laws; fractional Laplacian; entropy solutions; discontinuous Galerkin method; stability; high-order accuracy; convergence rate; JUMP-DIFFUSION-PROCESSES; INTEGRODIFFERENTIAL EQUATIONS; NUMERICAL SCHEMES; BURGERS EQUATIONS; CONVERGENCE; ASYMPTOTICS;
D O I：
10.1093/imanum/drq006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose, analyse and demonstrate a discontinuous Galerkin method for fractal conservation laws. Various stability estimates are established along with error estimates for regular solutions of linear equations. Moreover, in the nonlinear case and whenever piecewise constant elements are utilized, we prove a rate of convergence towards the unique entropy solution. We present numerical results for different types of solutions of linear and nonlinear fractal conservation laws.
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页码：1090 / 1122
页数：33
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