On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes

By Xiangxiong Zhang, Chi-Wang Shu. Journal of Computational Physics, 2010

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Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments (2014, background): “They can guarantee maximum principle in the scalar case [111, 115] and positivitypreserving for certain systems, for example positivity-preserving for density and pressure for Euler equations of compressible gas dynamics [112, 113, 115] and positivity-preserving for water height for shallow water eq”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, background): “For the most recent developments in the field of DG schemes see, for example, [116, 113, 117].”
Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems (2018, background): “We also refer the reader to Zhang and Shu [48, 50], Jiang and Liu [33] for recent/related developments in the context of dG methods.”
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains (2013, background): “This is not considered in the present work, but interested readers can refer to the work by Zhang and Shu [31].”