A Spectral Viscosity Method Based on Hermite Functions for Nonlinear Conservation Laws
نویسندگان
چکیده
We consider the approximation by a spectral method of the solution of the Cauchy problem for a scalar conservation law in one dimension posed in the whole real line. We analyze a spectral viscosity method in which the orthogonal basis considered is the one of Hermite functions. We prove the convergence of the approximate solution to the unique entropy solution of the problem by using compensated compactness arguments.
منابع مشابه
Spectral Viscosity Method with Generalized Hermite Functions and Its Spectral Filter for Nonlinear Conservation Laws
In this paper, we propose a new spectral viscosity method for the solution of nonlinear scalar conservation laws in the whole line. The proposed method is based on the generalized Hermite functions. It is shown rigorously that this scheme converges to the unique entropy solution by using compensated compactness arguments. The numerical experiments of the inviscid Burger’s equation support our r...
متن کاملChebyshev–legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws∗
In this paper, a super spectral viscosity method using the Chebyshev differential operator of high order Ds = ( √ 1− x2∂x) 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–Ga...
متن کاملChebyshev–legendre Spectral Viscosity Method for Nonlinear Conservation Laws∗
In this paper, a Chebyshev–Legendre spectral viscosity (CLSV) method is developed for nonlinear conservation laws with initial and boundary conditions. The boundary conditions are dealt with by a penalty method. The viscosity is put only on the high modes, so accuracy may be recovered by postprocessing the CLSV approximation. It is proved that the bounded solution of the CLSV method converges t...
متن کاملEntropy viscosity method for nonlinear conservation laws
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entr...
متن کاملComputer Methods in Applied Mechanics and Engineering 80 (1990) 197-208 North-holland Shock Capturing by the Spectral Viscosity Method*
A main disadvantage of using spectral methods for nonlinear conservation laws lies in the formation of Gibbs phenomenon, once spontaneous shock discontinuities appear in the solution. The global nature of spectral methods then pollutes the unstable Gibbs oscillations over all the computational domain, and the lack of entropy dissipation prevents convergences in these cases. In this paper, we di...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Numerical Analysis
دوره 46 شماره
صفحات -
تاریخ انتشار 2008