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• W3100603004 abstract "Abstract The methodology proposed in this paper bridges the gap between entropy stable and positivity-preserving discontinuous Galerkin (DG) methods for nonlinear hyperbolic problems. The entropy stability property and, optionally, preservation of local bounds for cell averages are enforced using flux limiters based on entropy conditions and discrete maximum principles, respectively. Entropy production by the (limited) gradients of the piecewise-linear DG approximation is constrained using Rusanov-type entropy viscosity. The Taylor basis representation of the entropy stabilization term reveals that it penalizes the solution gradients in a manner similar to slope limiting and requires implicit treatment to avoid severe time step restrictions. The optional application of a vertex-based slope limiter constrains the DG solution to be bounded by local maxima and minima of the cell averages. Numerical studies are performed for two scalar two-dimensional test problems with nonlinear and nonconvex flux functions." @default.
• W3100603004 created "2020-11-23" @default.
• W3100603004 creator A5090390734 @default.
• W3100603004 date "2021-10-20" @default.
• W3100603004 modified "2023-10-03" @default.
• W3100603004 title "Entropy stabilization and property-preserving limiters for ℙ₁ discontinuous Galerkin discretizations of scalar hyperbolic problems" @default.
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• W3100603004 doi "https://doi.org/10.1515/jnma-2020-0056" @default.
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