Third-order explicit Runge-Kutta discontinuous Galerkin method for linear conservation law with inflow boundary condition (Q639406)

The author examines the stability in \(L^{2}\)-norm and gives optimal a priori error estimate for 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 verify the above results.