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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu Province, P.R. China

    Qiang Zhang

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  1. Qiang Zhang
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Correspondence to Qiang Zhang.

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The research of this author is supported by NSFC grant 10871093.

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Zhang, Q. Third Order Explicit Runge-Kutta Discontinuous Galerkin Method for Linear Conservation Law with Inflow Boundary Condition. J Sci Comput 46, 294–313 (2011). https://doi.org/10.1007/s10915-010-9403-0

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  • DOI: https://doi.org/10.1007/s10915-010-9403-0

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