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 . The use of this estimate is not needed in a particular case of ()projection-based methods, and therefore the theoretical lack of convergence described does not exist in this case.

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Published on 10/09/19

DOI: 10.1007/s40324-018-0154-4
Licence: CC BY-NC-SA license

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