Minimal Stabilization for Discontinuous Galerkin Finite Element Methods for Hyperbolic Problems
Journal of Scientific Computing
Multidomain spectral method for the helically reduced wave equation
Journal of Computational Physics
Solution of the time-harmonic Maxwell equations using discontinuous Galerkin methods
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Analysis of an Interface Stabilized Finite Element Method: The Advection-Diffusion-Reaction Equation
SIAM Journal on Numerical Analysis
A robust SN-DG-approximation for radiation transport in optically thick and diffusive regimes
Journal of Computational Physics
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This paper presents a unified analysis of discontinuous Galerkin methods to approximate Friedrichs' systems. An abstract set of conditions is identified at the continuous level to guarantee existence and uniqueness of the solution in a subspace of the graph of the differential operator. Then a general discontinuous Galerkin method that weakly enforces boundary conditions and mildly penalizes interface jumps is proposed. All the design constraints of the method are fully stated, and an abstract error analysis in the spirit of Strang's Second Lemma is presented. Finally, the method is formulated locally using element fluxes, and links with other formulations are discussed. Details are given for three examples, namely, advection-reaction equations, advection-diffusion-reaction equations, and the Maxwell equations in the so-called elliptic regime.