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On hp convergence of stabilized finite element methods for the convection–diffusion equation

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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 \(p^2\). The use of this estimate is not needed in a particular case of (\(H^1\)-)projection-based methods, and therefore the theoretical lack of convergence described does not exist in this case.

Keywords

Convection-dominated flows High order interpolation Stabilized finite element methods 

Mathematics Subject Classification

65N30 

Notes

Acknowledgements

The author would like to acknowledge the support received from the ICREA Acadèmia Program, from the Catalan Government.

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Copyright information

© Sociedad Española de Matemática Aplicada 2018

Authors and Affiliations

  1. 1.Universitat Politècnica de CatalunyaBarcelonaSpain

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