Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier‐Stokes equations

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.