Approximation of the scalar convection-diffusion-reaction equation with stabilized finite element formulations of high order

In this paper we present stabilized finite element formulations to solve the scalar convection-diffusion-reaction equation in the case of small diffusion. On the one hand, we summarize the application of the ASGS and OSS formulations based on the concept of variational multiscale methods. On the other hand, we discuss aspects of the use of high order elements, focusing our numerical experiments on quadratic, cubic and fourth order elements. Likewise, the application of the OSS method requires the introduction of a projection, for which we introduce a modification of the fourth order simplicial element with an associated numerical integration rule.