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.


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