A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws

Juan Luo Nanjing University Chi-Wang Shu Brown University Qiang Zhang Nanjing University

Numerical Analysis and Scientific Computing mathscidoc:1610.25031

ESAIM: Mathematical Modelling and Numerical Analysis, 49, 991-1018, 2015
In this paper we present an {\em 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 $k\geq 2$. Quasi-optimal error estimate is obtained by energy techniques, for the so-called generalized E-fluxes under the standard temporal-spatial CFL condition $\tau\leq\gamma h$, 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.
Discontinuous Galerkin method, Runge-Kutta method, error estimates, symmetrizable system of conservation laws, energy analysis
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@inproceedings{juan2015a,
  title={A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws},
  author={Juan Luo, Chi-Wang Shu, and Qiang Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012034117467956149},
  booktitle={ESAIM: Mathematical Modelling and Numerical Analysis},
  volume={49},
  pages={991-1018},
  year={2015},
}
Juan Luo, Chi-Wang Shu, and Qiang Zhang. A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws. 2015. Vol. 49. In ESAIM: Mathematical Modelling and Numerical Analysis. pp.991-1018. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012034117467956149.
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