On the Conservation and Convergence to Weak Solutions of Global Schemes
Journal of Scientific Computing
The spectral signal processing suite
ACM Transactions on Mathematical Software (TOMS)
Chebyshev super spectral viscosity method for a fluidized bed model
Journal of Computational Physics
A spectral viscosity method for correcting the long-term behavior of POD models
Journal of Computational Physics
Spectral Vanishing Viscosity Method for Large-Eddy Simulation of Turbulent Flows
Journal of Scientific Computing
The Chebyshev-Legendre collocation method for a class of optimal control problems
International Journal of Computer Mathematics
Edge Detection Free Postprocessing for Pseudospectral Approximations
Journal of Scientific Computing
Journal of Scientific Computing
Hi-index | 0.01 |
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.