| Title:
|
Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries (English) |
| Author:
|
Hlaváček, Ivan |
| Author:
|
Křížek, Michal |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
1984 |
| Pages:
|
52-69 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined.
A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The internal approximation can be obtained by solving a system of linear algebraic equations with a positive definite matrix. (English) |
| Keyword:
|
dual variational methods |
| Keyword:
|
stream function |
| Keyword:
|
finite element |
| Keyword:
|
piecewise smooth boundary |
| Keyword:
|
dual problem |
| Keyword:
|
optimal rate of convergence |
| MSC:
|
35J25 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0543.65074 |
| idMR:
|
MR0729953 |
| DOI:
|
10.21136/AM.1984.104068 |
| . |
| Date available:
|
2008-05-20T18:24:04Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104068 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[4] B. M. Fraeijs de Veubeke M. Hogge: Dual analysis for heat conduction problems by finite elements.Internat. J. Numer. Methods Engrg. 5 (1972), 65-82. 10.1002/nme.1620050107 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
|
[9] M. Křížek: Conforming equilibrium finite element methods for some elliptic plane problems.RAIRO Anal. Numer. 17 (1983), 35--65. MR 0695451, 10.1051/m2an/1983170100351 |
| Reference:
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[10] O. A. Ladyzenskaya: The mathematical theory of viscous incompressible flow.Gordon & Breach, New York, 1969. MR 0254401 |
| Reference:
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[11] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
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[12] J. Nečas I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies: an introduction.Elsevier Scientific Publishing Company, Amsterdam, Oxford, New York, 1981. MR 0600655 |
| Reference:
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[13] P. Neittaanmäki J. Saranen: On finite element approximation of the gradient for solution of Poisson equation.Numer. Math. 37 (1981), 333-337. MR 0627107, 10.1007/BF01400312 |
| Reference:
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[14] J. Penman J. R. Fraser: Complementary and dual energy finite element principles in magnetostatics.IEEE Trans. on Magnetics 18 (1982), 319-324. 10.1109/TMAG.1982.1061883 |
| Reference:
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[15] G. Strang G. J. Fix: An analysis of the finite element method.Prentice Hall, New Jersey, 1973. MR 0443377 |
| Reference:
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[16] J. M. Thomas: Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes.Thesis, Université Paris VI, 1977. |
| Reference:
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[17] M. Zlámal: Curved elements in the finite element method.Čislennyje metody mechaniki splošnoj sredy, SO AN SSSR, 4 (1973), No. 5, 25-49. |
| Reference:
|
[18] M. Zlámal: Curved elements in the finite element method.SIAM J. Numer. Anal. 10 (1973), 229-240. MR 0395263, 10.1137/0710022 |
| . |
