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Space-time methods for hyperbolic conservation laws. (English) Zbl 0947.76055
Venkatakrishnan, V. (ed.) et al., Barriers and challenges in computational fluid dynamics. Proceedings of the ICASE/ LaRC workshop, Hampton, VA, USA, August 5-7, 1996. Dordrecht: Kluwer Academic Publishers. ICASE/LaRC Interdisciplinary Series in Science and Engineering. 6, 79-98 (1998).
Following the idea of compactness, the authors develop a time-accurate discontinuous Galerkin method. For any order of accuracy, the method is stable for Courant number less than 1, satisfies the entropy condition, and a minimization property. The method is tested on the linear scalar advection problem, on the Shu-Osher problem (Mach 3 shock propagating into a sinusoidal density wave), and on the problem on the pressure pulse in freestream over wall. Although the computation cost is high, the method has a strong theoretical foundation, many of its properties are highly desirable, and the authors hope that the future work should make the present method (or related methods) practical for a broader range of problems.
For the entire collection see [Zbl 0894.00051].
Reviewer: O.Titow (Berlin)

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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