Geodesic
On increasing the stability of the combined scheme of the discontinuous Galerkin method
Matematičeskoe modelirovanie, Tome 33 (2021) no. 3, pp. 98-108

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A special modification of the combined scheme of the discontinuous Galerkin method is proposed, which increases the stability of this scheme when calculating discontinuous solutions with shock waves. This modification is associated with the addition of an artificial viscosity of the fourth order of divergence to the basic scheme included in this combined scheme. Test calculations are presented. They demonstrate the advantages of the new combined scheme in comparison with the standard monotonized versions of the discontinuous Galerkin method.
Keywords: systems of conservation laws, combined schemes, discontinuous Galerkin method, artificial viscosity. 
@article{MM_2021_33_3_a6,
     author = {M. E. Ladonkina and O. A. Nekliudova and V. V. Ostapenko and V. F. Tishkin},
     title = {On increasing the stability of the combined scheme of the discontinuous {Galerkin} method},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {98--108},
     publisher = {mathdoc},
     volume = {33},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_3_a6/}
}
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M. E. Ladonkina; O. A. Nekliudova; V. V. Ostapenko; V. F. Tishkin. On increasing the stability of the combined scheme of the discontinuous Galerkin method. Matematičeskoe modelirovanie, Tome 33 (2021) no. 3, pp. 98-108. http://geodesic.mathdoc.fr/item/MM_2021_33_3_a6/