On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves

M. E. Ladonkina, O. A. Neklyudova, V. V. Ostapenko, V. F. Tishkin

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Abstract: The accuracy of the discontinuous Galerkin method of the third-order approximation on smooth solutions in the calculation of discontinuous solutions of a quasilinear hyperbolic system of conservation laws with shock waves propagating with a variable velocity is studied. As an example, the approximation of the system of conservation laws of shallow water theory is considered. On the example of this system, it is shown that, like the TVD and WENO schemes of increased order of approximation on smooth solutions, the discontinuous Galerkin method, despite its high accuracy on smooth solutions and in the localization of shock waves, reduces its order of convergence to the first order in the shock wave influence domain.

Original languageEnglish
Pages (from-to)1344-1353
Number of pages10
JournalComputational Mathematics and Mathematical Physics
Volume58
Issue number8
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

  • discontinuous Galerkin method
  • hyperbolic system of conservation laws
  • integral and local convergence order
  • shallow water theory
  • CONVERGENCE
  • DIFFERENCE-SCHEMES
  • HYPERBOLIC CONSERVATION-LAWS

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