Identifier: 2009-28
Author(s): Q. Zhang and C.-W. Shu
Title: Stability analysis and a priori error estimates to the third order explicit Runge-Kutta discontinuous Galerkin Method for scalar conservation laws
Page count: 33 pp.
Date: 2009-09-16
Abstract:
In this paper we present the analysis for the Runge-Kutta discon- tinuous Galerkin (RKDG) method to solve scalar conservation laws, where the time discretization is the third order explicit total variation diminishing Runge–Kutta (TVDRK3) method. We use an energy technique to present the L2-norm stability for scalar linear conservation laws, and obtain a priori error estimates for smooth solutions of scalar nonlinear conservation laws. Quasi-optimal order is obtained for general numerical fluxes, and optimal order is given for upwind fluxes. The theoret- ical results are obtained for piecewise polynomials with any degree k ≥ 1 under the standard temporal-spatial CFL condition τ ≤ γh, where h and τ, respectively, are the element length and time step, and the positive constant γ is independent of h and τ.
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