Implicit Runge-Kutta Methods and Discontinuous Galerkin Discretizations for Linear Maxwell's Equations

@article{Hochbruck2015ImplicitRM,
  title={Implicit Runge-Kutta Methods and Discontinuous Galerkin Discretizations for Linear Maxwell's Equations},
  author={Marlis Hochbruck and Tomislav Pazur},
  journal={SIAM J. Numer. Anal.},
  year={2015},
  volume={53},
  pages={485-507}
}
In this paper we consider implicit Runge--Kutta methods for the time integration of linear Maxwell's equations. We first present error bounds for the abstract Cauchy problem which respect the unboundedness of the differential operators using energy techniques. The error bounds hold for algebraically stable and coercive methods such as Gauss and Radau collocation methods. The results for the abstract evolution equation are then combined with a discontinuous Galerkin discretization in space using… 

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