Chebyshev-Legendre super spectral viscosity method for nonlinear conservation laws

被引：67

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.

引用

页码：893 / 908

页数：16

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