Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws
Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws
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DOI：
10.1137/s0036142995293912
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发表时间：
1998-06
影响因子：
2.9
通讯作者：
He-ping Ma
中科院分区：
文献类型：
--
作者：
He-ping Ma
利用高阶Chebyshev微分算子$D^s=（\sqrt{1-x^2} \opx）^s $建立了求解非线性守恒律方程的超谱粘性方法.边界条件用罚函数法处理。与二阶谱粘性方法相比，超谱粘性方法在保证Chebyshev-Galerkin、Chebyshev配置或Legendre-Galerkin逼近的有界解收敛性的同时，其收敛性要弱得多，并通过补偿紧性论证证明了这一点.
In this paper, a super spectral viscosity method using the Chebyshev differential operator of high order $D^s=(\sqrt{1-x^2} \opx)^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.