Nitsche’s method for general boundary conditions
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- by Mika Juntunen and Rolf Stenberg PDF
- Math. Comp. 78 (2009), 1353-1374 Request permission
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.References
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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
- 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.
- © Copyright 2008 American Mathematical Society
- Journal: Math. Comp. 78 (2009), 1353-1374
- MSC (2000): Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-08-02183-2
- MathSciNet review: 2501054