On the spectrum of discontinuous Galerkin methods for linear convection-diffusion equations
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We study the spectrum of certain discontinuous Galerkin (DG) methods of linear convection-diffusion PDEs. Specifically, we consider DG methods for a first order advection equation and for a second-order diffusion equation. Tight upper and lower bounds that we derive for the
spectrum can be used as quantifiers of the dissipation of the numerical solution and have implications for stability of the numerical scheme.