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2008-11

On the stability of finite element discretizations of convection--diffusion--reaction equations

by Knobloch, P., Tobiska, L..


Series: 2008-11, Preprints

MSC:
65N12 Stability and convergence of numerical methods
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

Abstract:
A priori error estimates for the local projection stabilization applied to
convection-diffusion-reaction equations are generally based on the coercivity
of the underlying bilinear form with respect to the local projection norm.
We show that the bilinear form of the local projection stabilization satisfies
an inf-sup condition in a stronger norm which is equivalent to
that of the streamline upwind/Petrov-Galerkin method. As a consequence
we get some insight in the stabilization mechanism of Galerkin discretizations
of higher order.

Keywords:
finite element method, convection-diffusio