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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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.
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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