A PRIORI ERROR ESTIMATES TO SMOOTH SOLUTIONS OF THE THIRD ORDER RUNGE-KUTTA DISCONTINUOUS GALERKIN METHOD FOR SYMMETRIZABLE SYSTEMS OF CONSERVATION LAWS

作者：Luo Juan^*; Shu Chi Wang; Zhang Qiang

来源：ESAIM: Mathematical Modelling and Numerical Analysis , 2015, 49(4): 991-1018.

DOI：10.1051/m2an/2014063

• Discontinuous Galerkin method
• Runge-Kutta method
• error estimates
• symmetrizable system of conservation laws
• energy analysis

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 tau <= gamma h, where h is the element length and tau is time step, and gamma is a positive constant independent of h and tau. Optimal estimates are also considered when the upwind numerical flux is used.

• 出版日期2015-8
• 单位南京大学