On the accuracy of discontinuous Galerkin method calculating gas-dynamic shock waves

Title	On the accuracy of discontinuous Galerkin method calculating gas-dynamic shock waves
Authors	M. E. Ladonkina^{1, 2}, O. A. Nekliudova^{1, 2}, V. V. Ostapenko², V. F. Tishkin^{1, 2} ¹Keldysh Institute of Applied Mathematics, Russian Academy of Sciences ²Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences
Annotation	We present the results of calculations of gas-dynamic shock waves, arising in solving the Cauchy problem with smooth periodic initial data. These calculations were carried out for three modifications of DG (Discontinuous Galerkin) method, in which the solution is represented as a piecewise linear discontinuous function. The results showed that DG methods, in which the Cockburn's limiter is applied to monotonize the obtained solution, have approximately the same accuracy in the areas of influence of shock waves, while the nonmonotonic DG method, in which this limiter is not used, demonstrates in these areas significantly higher accuracy. This allows the nonmonotonic DG method to be used as a basic one when constructing a combined scheme, which monotonously localizes the fronts of shock waves and at the same time preserves increased accuracy in the areas of their influence.
Keywords	gas dynamic equations, shock waves, discontinuous Galerkin method
Citation	Ladonkina M. E., Nekliudova O. A., Ostapenko V. V., Tishkin V. F. ''On the accuracy of discontinuous Galerkin method calculating gas-dynamic shock waves'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 121-128. Available at: https://conf.svmo.ru/files/2023/papers/paper18.pdf. - Date of access: 19.05.2024.

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On the accuracy of discontinuous Galerkin method calculating gas-dynamic shock waves

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