Abstract
Maximum principle or positivity-preserving property holds for many mathematical models. When the models are approximated numerically, it is preferred that these important properties can be preserved by numerical discretizations for the robustness and the physical relevance of the approximate solutions. In this paper, we investigate such discretizations of high order accuracy within the central discontinuous Galerkin framework. More specifically, we design and analyze high order maximum-principle-satisfying central discontinuous Galerkin methods for scalar conservation laws, and high order positivity-preserving central discontinuous Galerkin for compressible Euler systems. The performance of the proposed methods will be demonstrated through a set of numerical experiments.
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