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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
Published electronically: September 25, 2008
MathSciNet review: 2501054
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, and L. Donatella Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal. 39 (2001/02), no. 5, 1749-1779 (electronic). MR 1885715 (2002k:65183)
  • 2. Ivo Babuška, Uday Banerjee, and John E. Osborn, Survey of meshless and generalized finite element methods: a unified approach, Acta Numer. 12 (2003), 1-125. MR 2249154
  • 3. Roland Becker, Peter Hansbo, and Rolf Stenberg, A finite element methods for domain decomposition with non-matching grids, Mathematical Modelling and Numerical Analysis 37 (2003), no. 2, 209-225. MR 1991197 (2004e:65129)
  • 4. D. Braess and R. Verfürth, A posteriori error estimator for the Raviart-Thomas element, SIAM J. Numer. Anal 33 (1996), 2431-2444. MR 1427472 (97m:65201)
  • 5. Philippe G. Ciarlet, The finite element methods for elliptic problems, second ed., North-Holland, 1987. MR 0520174 (58:25001)
  • 6. J.A. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 36 (1970/71), 9-15. MR 0341903 (49:6649)
  • 7. Rolf Stenberg, Mortaring by a method of J.A. Nitsche, Computational Mechanics; New Trends and Applications, S. Idelsohn, E. Oñate and E. Dvorkin (Eds.) (CIMNE, Barcelona, Spain, 1998). MR 1839048
  • 8. Rüdiger Verfürth, A review of a posteriori error estimation and adaptive mesh refinement techniques, Wiley, 1996.

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Additional Information

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

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.
Article copyright: © Copyright 2008 American Mathematical Society

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