On hp convergence of stabilized finite element methods for the convection–diffusion equation
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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.
KeywordsConvection-dominated flows High order interpolation Stabilized finite element methods
Mathematics Subject Classification65N30
The author would like to acknowledge the support received from the ICREA Acadèmia Program, from the Catalan Government.
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