Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems

@article{Cockburn2000RungeKuttaDG,
  title={Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems},
  author={Bernardo Cockburn and Chi-Wang Shu},
  journal={Journal of Scientific Computing},
  year={2000},
  volume={16},
  pages={173-261}
}
In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge–Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization… CONTINUE READING
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