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In this paper, a super spectral viscosity method using the Chebyshev differential operator of high order D s = ( √ 1 − x 2 ∂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 conservationdoi:10.1137/s0036142995293912 fatcat:ntsaqnli3fedvfuigccfi5sgiq