2006/01/01 by Qiang Zhang, Chi‐Wang Shu · 1 citation
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations
paper · doi:10.1137/040620382
In this paper we study the error estimates to sufficiently smooth solutions of symmetrizable systems of conservation laws for the Runge–Kutta discontinuous Galerkin (RKDG) method. Time discretization is the second‐order explicit TVD (total variation diminishing) Runge–Kutta method, and the ℙk (piecewise polynomial) finite element is used. When k=1 (piecewise linear finite element), the error estimate is obtained under the usual CFL condition \dt≤ β h for nonlinear systems in one dimension and for linear systems in multiple space dimensions. Here, h is the maximum element length, τ is the time step, and β is a positive constant independent of h and τ. Error estimates for ℙk finite elements with k>1 are obtained under a more restrictive CFL condition.