## Abstract

This work analyzes some aspects of the hp convergence of stabilized finite element methods for the convection-diffusion equation when diffusion is small. The methods discussed are classical-residual based stabilization techniques and also projection-based stabilization methods. The theoretical impossibility of obtaining an optimal convergence rate in terms of the polynomial order p for all possible Péclet numbers is explained. The key point turns out to be an inverse estimate that scales as ${\displaystyle p^{2}}$ . The use of this estimate is not needed in a particular case of (${\displaystyle H^{1}-}$)projection-based methods, and therefore the theoretical lack of convergence described does not exist in this case.

### Document information

Published on 10/09/19

DOI: 10.1007/s40324-018-0154-4