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Application of the RKDG method for gas dynamics problems. (Russian. English summary) Zbl 1313.76090

Galerkin’s method with discontinuous base functions has a high order of accuracy. In the case of a strong discontinuity, constraining inclinations terms, i.e., limiters, are usually introduced to get a monotonous solution by the method. The limiters can negatively influence the solution accuracy. Here, the question about the order preserving and monotony of the solution accuracy ensuring are investigated.

MSC:

76N15 Gas dynamics (general theory)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
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