Weighting the edge stabilization

Alexandre Ern (1) , Jean-Luc Guermond (2, 3)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 Department of Mathematics and Statistics [Texas Tech]
3 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur

A modification of the edge stabilization technique is proposed to improve the behavior of the method when solving conservation equations with non-smooth data and/or non-smooth solutions. The key ingredient is tempering the edge stabilization in regions of large gradients through appropriate weights. The new method is shown to preserve the convergence properties of the original method on smooth solutions and numerical tests indicate that it performs better on non-smooth solutions.

Keywords: finite elements; conservation equations; edge stabilization; linear stabilization; nonlinear viscosity

Domains: Numerical Analysis [math.NA]

Alexandre Ern, Jean-Luc Guermond. Weighting the edge stabilization. 2012. ⟨hal-00674336⟩