The convergence of the finite element method for boundary value problems of the system of elliptic equations

Alexander Ženíšek

Aplikace matematiky (1969)

  • Volume: 14, Issue: 5, page 355-377
  • ISSN: 0862-7940

Abstract

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The finite element method is a generalized Ritz method using special admissible functions. In the paper, triangular elements and functions are considered which are linear or quadratic polynomials on each triangle. The convergence is proved for variational problems arising from second order boundary value problems. The order of accuracy of the procedure is ( s + 1 ) / 2 in case of inhomogeneous Dirichlet conditions and s in other cases ( s is the degree of the polynomial used).

How to cite

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Ženíšek, Alexander. "Konvergence metody konečných prvků pro okrajové problémy systému eliptických rovnic." Aplikace matematiky 14.5 (1969): 355-377. <http://eudml.org/doc/14612>.

@article{Ženíšek1969,
author = {Ženíšek, Alexander},
journal = {Aplikace matematiky},
keywords = {numerical analysis},
language = {cze},
number = {5},
pages = {355-377},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Konvergence metody konečných prvků pro okrajové problémy systému eliptických rovnic},
url = {http://eudml.org/doc/14612},
volume = {14},
year = {1969},
}

TY - JOUR
AU - Ženíšek, Alexander
TI - Konvergence metody konečných prvků pro okrajové problémy systému eliptických rovnic
JO - Aplikace matematiky
PY - 1969
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 14
IS - 5
SP - 355
EP - 377
LA - cze
KW - numerical analysis
UR - http://eudml.org/doc/14612
ER -

References

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  11. С. Г. Михлин X. Л. Смолицкий, Приближенные методы решения дифференциальных и интегральных уравнений, Москва 1965. (1965) Zbl1225.00032
  12. J. Kratochvíl a F. Leitner, Metoda konečných prvků a její aplikace v rovinných úlohách pružnosti, Stavebnícky časopis 16 (1968), 2, 65 - 82; 4, 201 - 217. (1968) 
  13. A. Ženíšek, Konvergence posloupnosti přibližných řešení při metodě konečných prvků s trojúhelníkovým tvarem, Stavebnícky časopis 16 (1968), 577-591. (1968) 
  14. A. Ženíšek, Interpolační polynomy na trojúhelníku a čtyřstěnu a metoda konečných prvků, (zasláno do Aplikací matematiky). 

Citations in EuDML Documents

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  1. Jan Brandts, Sergey Korotov, Michal Křížek, Generalization of the Zlámal condition for simplicial finite elements in ℝ d
  2. Kenta Kobayashi, Takuya Tsuchiya, A priori error estimates for Lagrange interpolation on triangles
  3. Michal Křížek, On semiregular families of triangulations and linear interpolation
  4. Václav Kučera, Several notes on the circumradius condition
  5. Michal Křížek, Professor Alexander Ženíšek passed away
  6. Antti Hannukainen, Sergey Korotov, Michal Křížek, On Synge-type angle condition for d -simplices
  7. Ali Khademi, Sergey Korotov, Jon Eivind Vatne, On interpolation error on degenerating prismatic elements

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