CHEBYSHEV-LEGENDRE SUPER SPECTRAL VISCOSITY METHOD FOR NONLINEAR CONSERVATION-LAWS

In this paper, a super spectral viscosity method using the Chebyshev d ifferential operator of high order D-s = (root 1-x(2) partial derivati ve(x))(s) is developed for nonlinear conservation laws. The boundary c onditions are treated by a penalty method. Compared with the second-or der spectral viscosity method, the super one is much weaker while stil l guaranteeing the convergence of the bounded solution of the Chebyshe v-Galerkin, Chebyshev collocation, or Legendre-Galerkin approximations to nonlinear conservation laws, which is proved by compensated compac tness arguments.