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Nitsche's method for general boundary conditions
Author(s):
Mika
Juntunen;
Rolf
Stenberg.
Journal:
Math. Comp.
78
(2009),
1353-1374.
MSC (2000):
Primary 65N30
Posted:
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.
References:
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- 1.
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- 3.
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- Philippe G. Ciarlet, The finite element methods for elliptic problems, second ed., North-Holland, 1987. MR 0520174 (58:25001)
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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:
10.1090/S0025-5718-08-02183-2
PII:
S 0025-5718(08)02183-2
Received by editor(s):
October 17, 2007,
Received by editor(s) in revised form:
May 21, 2008
Posted:
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 of article:
Copyright
2008,
American Mathematical Society
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