L₂ estimates for Chebyshev collocation

Abstract

We study Chebyshev collocation when applied to a system of symmetric hyperbolic equations on a finite domain with general boundary conditions. We show that the use of orthogonal projections in the L2 norm in order to smooth out the higher modes and to implement boundary conditions leads to a stable numerical approximation in the L2 norm; the stability estimate corresponds to the estimate of the continuous problem. For constant coefficient systems the method reduces to an efficient implementation of Legendre-Galerkin. © 1988 Plenum Publishing Corporation.