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We study a family of generalized slope limiters in two dimensions forRunge-Kutta discontinuous Galerkin (RKDG) solutions of advection--diffusionsystems. We analyze the numerical behavior of these limiters applied to a pairof model problems, comparing the error of the approximate solutions, anddiscuss each limiter's advantages and disadvantages. We then introduce a seriesof coupled $p$-enrichment schemes that may be used as standalone dynamic$p$-enrichment strategies, or may be augmented via any in the family ofvariable-in-$p$ slope limiters presented.

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