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Nitsche's method for general boundary conditions


Authors: Mika Juntunen and Rolf Stenberg
Journal: Math. Comp. 78 (2009), 1353-1374
MSC (2000): Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-08-02183-2
Published electronically: September 25, 2008
MathSciNet review: 2501054
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Abstract: We introduce a method for treating general boundary conditions in the finite element method generalizing an approach, due to Nitsche (1971), for approximating Dirichlet boundary conditions. We use Poisson's equations as a model problem and prove a priori and a posteriori error estimates. The method is also compared with the traditional Galerkin method. The theoretical results are verified numerically.


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Additional Information

Mika Juntunen
Affiliation: Institute of Mathematics, Helsinki University of Technology, P. O. Box 1100, 02015 TKK, Finland
Email: mika.juntunen@tkk.fi

Rolf Stenberg
Affiliation: Institute of Mathematics, Helsinki University of Technology, P. O. Box 1100, 02015 TKK, Finland

DOI: https://doi.org/10.1090/S0025-5718-08-02183-2
Received by editor(s): October 17, 2007
Received by editor(s) in revised form: May 21, 2008
Published electronically: September 25, 2008
Additional Notes: This work was supported by the Finnish National Graduate School in Engineering Mechanics, by the Academy of Finland, and TEKES, the National Technology Agency of Finland.
Article copyright: © Copyright 2008 American Mathematical Society