Numerische Mathematik

, Volume 99, Issue 1, pp 1–24 | Cite as

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

  • S. Bartels
  • C. CarstensenEmail author
  • G. Dolzmann


The numerical solution of elliptic boundary value problems with finite element methods requires the approximation of given Dirichlet data u D by functions u D,h in the trace space of a finite element space on Γ D . In this paper, quantitative a priori and a posteriori estimates are presented for two choices of u D,h , namely the nodal interpolation and the orthogonal projection in L2 D ) 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.


Finite Element Method Orthogonal Projection Posteriori Error Element Space Elliptic Boundary 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsHumboldt-Universität zu BerlinBerlinGermany

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