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

• Ramon Codina ^[1]
  1. [1] Universidad Politécnica de Cataluña
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 75, Nº. Extra 4, 2018 (Ejemplar dedicado a: Variational Multiscale Methods), págs. 591-606
• Idioma: inglés
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• Resumen

  • 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 p2. The use of this estimate is not needed in a particular case of (H1-)projection-based methods, and therefore the theoretical lack of convergence described does not exist in this case.