### 2007-41

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

Series: 2007-41, Preprints

MSC:
65N15 Error bounds
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65N50 Mesh generation and refinement

Abstract:
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 $\varepsilon$.
Performing numerical experiments,
it turns out that strongly imposed Dirichlet boundary conditions lead to
the whole boundary in an $\varepsilon$-weighted weak sense due to Nitsche