Curved triangular finite C m -elements

Alexander Ženíšek

Aplikace matematiky (1978)

  • Volume: 23, Issue: 5, page 346-377
  • ISSN: 0862-7940

Abstract

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Curved triangular C m -elements which can be pieced together with the generalized Bell’s C m -elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order 2 ( m + 1 ) in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same as in the case of polygonal domains when the generalized Bell’s C m -elements are used.

How to cite

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Ženíšek, Alexander. "Curved triangular finite $C^m$-elements." Aplikace matematiky 23.5 (1978): 346-377. <http://eudml.org/doc/15064>.

@article{Ženíšek1978,
abstract = {Curved triangular $C^m$-elements which can be pieced together with the generalized Bell’s $C^m$-elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order $2(m+1)$ in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same as in the case of polygonal domains when the generalized Bell’s $C^m$-elements are used.},
author = {Ženíšek, Alexander},
journal = {Aplikace matematiky},
keywords = {generalized Bell’s $C^m$-elements; approximate solution; rate of convergence; generalized Bell's Cm-elements; approximate solution; rate of convergence},
language = {eng},
number = {5},
pages = {346-377},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Curved triangular finite $C^m$-elements},
url = {http://eudml.org/doc/15064},
volume = {23},
year = {1978},
}

TY - JOUR
AU - Ženíšek, Alexander
TI - Curved triangular finite $C^m$-elements
JO - Aplikace matematiky
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 5
SP - 346
EP - 377
AB - Curved triangular $C^m$-elements which can be pieced together with the generalized Bell’s $C^m$-elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order $2(m+1)$ in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same as in the case of polygonal domains when the generalized Bell’s $C^m$-elements are used.
LA - eng
KW - generalized Bell’s $C^m$-elements; approximate solution; rate of convergence; generalized Bell's Cm-elements; approximate solution; rate of convergence
UR - http://eudml.org/doc/15064
ER -

References

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  1. Bramble J. H., Zlámal M., Triangular elements in the finite element method, Math. Соmр. 24 (1970), 809-820. (1970) MR0282540
  2. Ciarlet P. G., Raviart P. A., The combined effect of curved boundaries and numerical integration in isoparametric finite element methods, In: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, Editor), pp. 409-474, Academic Press, New York 1972. (1972) Zbl0262.65070MR0421108
  3. Ciarlet P. G., Numerical Analysis of the Finite Element Method, Université de Montréal, 1975. (1975) MR0495010
  4. Holuša L., Kratochvíl J., Zlámal M., Ženíšek A., The Finite Element Method, Technical Report. Computing Center of the Technical University of Brno, 1970. (In Czech.) (1970) 
  5. Kratochvíl J., Ženíšek A., Zlámal M., 10.1002/nme.1620030409, Int. J. numer. Meth. Engng. 3 (1971), 553 - 563. (1971) Zbl0248.73029DOI10.1002/nme.1620030409
  6. Mansfield L., 10.1137/0715037, SIAM J. Numer. Anal. 15 (1978), the June issue. (1978) Zbl0391.65047MR0471373DOI10.1137/0715037
  7. Nečas J., Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  8. Stroud A. H., Approximate Calculation of Multiple Integrals, Prentice-Hall., Englewood Cliffs, N. J., 1971. (1971) Zbl0379.65013MR0327006
  9. Zlámal M., 10.1002/nme.1620050307, Int. J. numer. Meth. Engng. 5 (1973), 367-373. (1973) Zbl0254.65073MR0395262DOI10.1002/nme.1620050307
  10. Zlámal M., 10.1137/0710022, SIAM J. Numer. Anal. 10(1973), 229-240. (1973) Zbl0285.65067MR0395263DOI10.1137/0710022
  11. Zlámal M., 10.1137/0711031, SlAM J. Numer. Anal. 1.1 (1974), 347-362. (1974) Zbl0277.65064MR0343660DOI10.1137/0711031
  12. Ženíšek A., 10.1007/BF02165119, Numer. Math. 15 (1970), 283 - 296. (1970) Zbl0216.38901MR0275014DOI10.1007/BF02165119

Citations in EuDML Documents

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  1. Alexander Ženíšek, Discrete forms of Friedrichs' inequalities in the finite element method
  2. Alexander Ženíšek, Nonhomogeneous boundary conditions and curved triangular finite elements
  3. Jitka Křížková, Special exact curved finite elements
  4. Dana Říhová-Škabrahová, Linear scheme for finite element solution of nonlinear parabolic-elliptic problems with nonhomogeneous Dirichlet boundary condition
  5. Josef Nedoma, The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements
  6. Alexander Ženíšek, How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes
  7. Alexander Ženíšek, Finite element methods for coupled thermoelasticity and coupled consolidation of clay
  8. Jiří Hřebíček, Numerical analysis of the general biharmonic problem by the finite element method
  9. Ivan Hlaváček, Michal Křížek, Internal finite element approximation in the dual variational method for the biharmonic problem
  10. Jozef Kačur, Alexander Ženíšek, Analysis of approximate solutions of coupled dynamical thermoelasticity and related problems

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