On the accuracy of the discontinuous Galerkin method inside centered rarefaction waves and in the areas of their influence

On the accuracy of the discontinuous Galerkin method inside centered rarefaction waves and in the areas of their influence Full article

Journal

Mathematical Models and Computer Simulations
ISSN: 2070-0482

Output data

Year: 2025, Volume: 17, Number: 3, Pages: 326-337 Pages count : 12 DOI: 10.1134/S2070048225700073

Tags

shallow water equations, centered rarefaction waves, discontinuous Galerkin method

Authors

Ladonkina M.E. ¹ , Ostapenko V.V. ² , Tishkin V.F. ¹ , Khandeeva N.A ²

Affiliations

1	Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
2	Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

The accuracy of two schemes of the discontinuous Galerkin method with piecewise linear solutions is investigated when calculating the special Cauchy problem for shallow water equations with discontinuous initial data, the exact solution of which contains a centered rarefaction wave and does not contain a shock wave. It is shown that inside the centered rarefaction wave and in the area of its influence, the solutions of both schemes with different orders converge to different invariants of the exact solution, which leads to a decrease in the accuracy of these schemes when calculating the vector of the basic variables of the considered Cauchy problem

Ladonkina M.E. , Ostapenko V.V. , Tishkin V.F. , Khandeeva N.A.
On the accuracy of the discontinuous Galerkin method inside centered rarefaction waves and in the areas of their influence
Mathematical Models and Computer Simulations. 2025. V.17. N3. P.326-337. DOI: 10.1134/S2070048225700073 Scopus

Ладонкина М.Е. , Остапенко В.В. , Тишкин В.Ф. , Хандеева Н.А.
О точности разрывного метода Галеркина внутри центрированных волн разрежения и в областях их влияния
Математическое моделирование. 2025. Т.37. №1. С.113-130. РИНЦ

Submitted:	Aug 26, 2024
Accepted:	Oct 14, 2024

Scopus:

2-s2.0-105010184373

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