A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws

In this paper we present an a priori error estimate of the Runge-Kutta discontinuous Galerkin method for solving symmetrizable conservation laws, where the time is discretized with the third order explicit total variation diminishing Runge-Kutta method and the finite element space is made up of piecewise polynomials of degree k ≥ 2. Quasi-optimal error estimate is obtained by energy techniques, for the so-called generalized E-fluxes under the standard temporal-spatial CFL condition τ ≤ γh, where h is the element length and τ is time step, and γ is a positive constant independent of h and τ . Optimal estimates are also considered when the upwind numerical flux is used.