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Elsevier, Journal of Computational Physics, 22(230), p. 8028-8056

DOI: 10.1016/j.jcp.2011.07.009

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Adaptive hierarchic transformations for dynamically $p$-enriched slope-limiting over discontinuous Galerkin systems of generalized equations

Journal article published in 2010 by C. Michoski ORCID, C. Mirabito, C. Dawson, E. J. Kubatko, D. Wirasaet, J. J. Westerink
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This paper is available in a repository.

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Abstract

We study a family of generalized slope limiters in two dimensions for Runge-Kutta discontinuous Galerkin (RKDG) solutions of advection--diffusion systems. We analyze the numerical behavior of these limiters applied to a pair of model problems, comparing the error of the approximate solutions, and discuss each limiter's advantages and disadvantages. We then introduce a series of coupled $p$-enrichment schemes that may be used as standalone dynamic $p$-enrichment strategies, or may be augmented via any in the family of variable-in-$p$ slope limiters presented. ; Comment: 39 pages, 8 figures, 3 tables