Error Estimates Of The Third Order Explicit RKDG Method For A Linear Hyperbolic Equation In 1-d With Discontinuous Initial Data

In this paper,we present an error estimate for the explicit Runge-Kutta discontin-uous Galerkin method based on the generalized alternating numerical fluxes in solving one-dimensional linear hyperbolic equation with discontinuous but piecewise smooth initial data.The discontinuous finite element space is made up of piecewise polyno-mials of arbitrary degree k?1,and time is advanced by the third order explicit total variation diminishing Runge-Kutta method under the standard CFL temporal-spatial condition.We proved that the L2(R\RT)-norm error at the final time T is optimal in both space and time,where RT is the pollution region due to the discontinuity of the initial value,with the width of O((?)log(1/h)),Here h is the maximum cell length and ? is the flowing speed.The results are independent of the weight number ?in the numerical flux and the time step.Numerical experiments validating these results are presented.