On the role of boundary conditions for CIP stabilization of higher order finite elements

We investigate the Continuous Interior Penalty (CIP) stabilization method for higher order finite elements applied to a convection diffusion equation with a small diffusion parameter s. Performing numerical experiments, it turns out that strongly imposed Dirichlet boundary conditions lead to relativ...

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Bibliographic Details
Published inElectronic transactions on numerical analysis Vol. 32; p. 1
Main Author Schieweck, Friedhelm
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.01.2008
Subjects
Boundary value problems
Differential equations, Partial
Equations
Numerical analysis
Germany
Online AccessGet full text
ISSN1068-9613
1097-4067

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Summary:We investigate the Continuous Interior Penalty (CIP) stabilization method for higher order finite elements applied to a convection diffusion equation with a small diffusion parameter s. Performing numerical experiments, it turns out that strongly imposed Dirichlet boundary conditions lead to relatively bad numerical solutions. However, if the Dirichlet boundary conditions are imposed on the inflow part of the boundary in a weak sense and additionally on the whole boundary in an ζ-weighted weak sense due to Nitsche then one obtains reasonable numerical results. In many cases, this holds even in the limit case where the parameter of the CIP stabilization is zero, i.e., where the standard Galerkin discretization is applied. We present an analysis which explains this effect. Key words. diffusion-convection-reaction equation, finite elements, Nitsche type boundary conditions, error estimates AMS subject classifications. 65N15, 65N30, 65N50
ISSN:1068-9613
1097-4067