02-1   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Sören Bartels, Carsten Carstensen, Georg Dolzmann:

Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis

The finite element analysis of elliptic boundary value problems involves the approximation of the given boundary data. If the Dirichlet data are not contained in the finite element space, then the resulting approximation error affects a priori and a~posteriori error estimates. This error contribution is of higher order in H1 error estimates for the standard nodal interpolation of the given Dirichlet data. A model example demonstrates that this is not the case in L2 error estimates. We therefore propose the use of the L2 projection onto the induced finite element space on the Dirichlet boundary. We show that for an elliptic model equation in two and three dimensions the boundary contribution is then of higher order in a priori and a~posteriori H1 and L2 error estimates.

Mathematics Subject Classification (1991): 65N30, 65R20, 73C50

Keywords: finite element methods, a posteriori error estimates, Dirichlet conditions, data approximation

Mail an Jens Burmeister
[Thu Feb 19 18:56:36 2009]