Adaptive hierarchic transformations for dynamically $p$-enriched slope-limiting over discontinuous Galerkin systems of generalized equations
arXiv:1012.5826 · doi:10.1016/j.jcp.2011.07.009
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.
39 pages, 8 figures, 3 tables