Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems

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Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems (2003)

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by Robert M. Kirby , George Em Karniadakis

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@MISC{Kirby03selectingthe,
    author = {Robert M. Kirby and George Em Karniadakis},
    title = {Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems},
    year = {2003}
}

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Abstract

In this paper we present numerical investigations of four different formulations of the discontinuous Galerkin method for diffusion problems. Our focus is to determine, through numerical experimentation, practical guidelines as to which numerical flux choice should be used when applying discontinuous Galerkin methods to such problems. We examine first an inconsistent and weakly unstable scheme analyzed in Zhang and Shu, Math. Models Meth. Appl. Sci.(M 3 AS) 13, 395–413 (2003), and then proceed to examine three consistent and stable schemes: the Bassi–Rebay scheme (J. Comput. Phys. 131, 267 (1997)), the local

Keyphrases

discontinuous galerkin method diffusion problem numerical flux numerical flux choice basso rebay scheme stable scheme practical guideline weakly unstable scheme numerical experimentation different formulation model meth present numerical investigation

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