Chebyshev-Legendre super spectral viscosity method for nonlinear conservation laws

被引：65
|
作者：
Ma, HP [1 ]
机构：
[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA
[2] Shanghai Univ Sci & Technol, Dept Math, Shanghai 201800, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 1998年 / 35卷 / 03期
关键词：
conservation laws; Chebyshev-Legendre method; super spectral viscosity; convergence;
D O I：
10.1137/S0036142995293912
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a super spectral viscosity method using the Chebyshev differential operator of high order D-s = (root 1-x(2) partial derivative(x))(s) is developed for nonlinear conservation laws. The boundary conditions are treated by a penalty method. Compared with the second-order spectral viscosity method, the super one is much weaker while still guaranteeing the convergence of the bounded solution of the Chebyshev-Galerkin, Chebyshev collocation, or Legendre-Galerkin approximations to nonlinear conservation laws, which is proved by compensated compactness arguments.
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页码：893 / 908
页数：16
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