Residual-based stabilized higher-order FEM for advection-dominated problems

We reconsider the numerical solution of linear(ized) advection–diffusion–reaction problems using higher-order finite elements together with stabilized Galerkin methods of streamline-diffusion type (SUPG) and with shock-capturing stabilization. The analysis improves the a priori analysis in our previous paper [T. Knopp, G. Lube, G. Rapin, Stabilized finite element methods with shock capturing for advection–diffusion problems, Comput. Methods Appl. Mech. Engrg. 191 (2002) 2997–3013]. The theoretical results are supported by some numerical experiments.