Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws. (English) Zbl 1129.65062
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.
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.
Reviewer: Etienne Emmrich (Berlin)
MSC:
65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
35L65 | Hyperbolic conservation laws |
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |