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On the discontinuous Galerkin method for the numerical solution of compressible high-speed flow. (English) Zbl 1276.76039
Brezzi, Franco (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, the 4th European conference, Ischia, July 2001. Berlin: Springer (ISBN 88-470-0180-3/hbk). 65-83 (2003).
Summary: The paper deals with an application of the discontinuous Galerkin finite element (DG-FE) method to the numerical solution of a system of hyperbolic equations. We extend our results (with C. Schwab) from [Calcolo 39, No. 1, 1–40 (2002; Zbl 1098.65095), Math. Comput. Simul. 61, No. 3–6, 333–346 (2003; Zbl 1013.65108)], where two versions of the DG-FE method were applied to the scalar convection-diffusion equation. In order to avoid spurious oscillations near discontinuities we develop a new limiting which is based on the control of interelement jumps and switches from piecewise linear to piecewise constant approximations. Isoparametric finite elements are used near a curved boundary of nonpolygonal computational domain in order to achieve a physically admissible and sufficiently accurate numerical solution. Numerical examples of transonic flow through the GAMM channel and around the NACA0012 airfoil are presented. Finally, we mention some theoretical results obtained for a modified DG-FE method applied to a nonlinear convection-diffusion problem.
For the entire collection see [Zbl 1013.00024].

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