Geodesic
Entropic regularization of the discontinuous Galerkin method for two-dimensional Euler equations in triangulated domains
Matematičeskoe modelirovanie, Tome 35 (2023) no. 3, pp. 3-19

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An entropic regularization of the discontinuous Galerkin method in conservative variables is constructed for the two-dimensional Euler equations in domains divided into non-regular triangular cells. Based on the use of local orthogonal linear basis functions in a triangular cell, a new slope limiter is proposed. In order to ensure the fulfillment of the discrete analogue of the entropic inequality in a triangular cell, a special slope limiter is constructed.
Mots-clés : Euler equations
Keywords: the discontinuous Galerkin method, conservation laws, slope limiter, entropic inequality. 
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     author = {Yu. A. Kriksin and V. F. Tishkin},
     title = {Entropic regularization of the discontinuous {Galerkin} method for two-dimensional {Euler} equations in triangulated domains},
     journal = {Matemati\v{c}eskoe modelirovanie},
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     publisher = {mathdoc},
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     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/MM_2023_35_3_a0/}
}
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Yu. A. Kriksin; V. F. Tishkin. Entropic regularization of the discontinuous Galerkin method for two-dimensional Euler equations in triangulated domains. Matematičeskoe modelirovanie, Tome 35 (2023) no. 3, pp. 3-19. http://geodesic.mathdoc.fr/item/MM_2023_35_3_a0/