Third Order Explicit Runge-Kutta Discontinuous Galerkin Method for Linear Conservation Law with Inflow Boundary Condition

Authors:
Qiang Zhang
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093
Venue:
Journal of Scientific Computing
Year:
2011

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Abstract

In this paper we will present the stability in L2-norm and the optimal a priori error estimate for the Runge-Kutta discontinuous Galerkin method to solve linear conservation law with inflow boundary condition. Semi-discrete version and fully-discrete version of this method are considered respectively, where time is advanced by the explicit third order total variation diminishing Runge-Kutta algorithm. To avoid the reduction of accuracy, two correction techniques are given for the intermediate boundary condition. Numerical experiments are also given to verify the above results.