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

Authors:
S. Bartels;C. Carstensen;G. Dolzmann
Affiliations:
University of Maryland, Mathematics Department, 20742-4015, College Park, MD, USA;Humboldt-Universität zu Berlin, Department of Mathematics, Unter den Linden 6, 10099, Berlin, MD, Germany;University of Maryland, Mathematics Department, 20742-4015, College Park, MD, USA
Venue:
Numerische Mathematik
Year:
2004

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Abstract

The numerical solution of elliptic boundary value problems with finite element methods requires the approximation of given Dirichlet data uD by functions uD,h in the trace space of a finite element space on ΓD. In this paper, quantitative a priori and a posteriori estimates are presented for two choices of uD,h, namely the nodal interpolation and the orthogonal projection in L2(ΓD) onto the trace space. Two corresponding extension operators allow for an estimate of the boundary data approximation in global H1 and L2 a priori and a posteriori error estimates. The results imply that the orthogonal projection leads to better estimates in the sense that the influence of the approximation error on the estimates is of higher order than for the nodal interpolation.