The authors continue their work on the numerical approximation of symmetrizable systems of hyperbolic conservation laws. The method under consideration here is the Runge-Kutta discontinuous Galerkin method with an explicit second-order total variation diminishing Runge-Kutta time discretization and a (higher-order) discontinuous Galerkin discretization in space.
Assuming the existence of a sufficiently smooth exact solution, sufficiently smooth fluxes with bounded derivatives, and the numerical fluxes being generalized E-fluxes, error estimates in the \(L^{\infty}(L^2)\)-norm are derived if a CFL condition is fulfilled. Whereas for linear finite elements, the CFL condition is the usual one, higher-order elements require a more restrictive CFL condition.