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Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations. (English) Zbl 0638.76080

SUPG methods were originally developed for the scalar advection-diffusion equation and the incompressible Navier-Stokes equations. In the last few years successful extensions have been made to symmetric advective- diffusive systems and, in particular, the compressible Euler and Navier- Stokes equations. New procedures have been introduced to improve resolution of discontinuities and thin layers. In this paper a brief overview is presented of recent progress in the development and understanding of SUPG methods.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76N15 Gas dynamics (general theory)
65Z05 Applications to the sciences
35Q30 Navier-Stokes equations
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