# Curved triangular finite ${C}^{m}$-elements

Aplikace matematiky (1978)

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

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topŽeníšek, 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

top- Bramble J. H., Zlámal M., Triangular elements in the finite element method, Math. Соmр. 24 (1970), 809-820. (1970) MR0282540
- 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
- Ciarlet P. G., Numerical Analysis of the Finite Element Method, Université de Montréal, 1975. (1975) MR0495010
- 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)
- Kratochvíl J., Ženíšek A., Zlámal M., 10.1002/nme.1620030409, Int. J. numer. Meth. Engng. 3 (1971), 553 - 563. (1971) DOI10.1002/nme.1620030409
- Mansfield L., 10.1137/0715037, SIAM J. Numer. Anal. 15 (1978), the June issue. (1978) Zbl0391.65047MR0471373DOI10.1137/0715037
- Nečas J., Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
- Stroud A. H., Approximate Calculation of Multiple Integrals, Prentice-Hall., Englewood Cliffs, N. J., 1971. (1971) Zbl0379.65013MR0327006
- Zlámal M., 10.1002/nme.1620050307, Int. J. numer. Meth. Engng. 5 (1973), 367-373. (1973) MR0395262DOI10.1002/nme.1620050307
- Zlámal M., 10.1137/0710022, SIAM J. Numer. Anal. 10(1973), 229-240. (1973) MR0395263DOI10.1137/0710022
- Zlámal M., 10.1137/0711031, SlAM J. Numer. Anal. 1.1 (1974), 347-362. (1974) MR0343660DOI10.1137/0711031
- Ženíšek A., 10.1007/BF02165119, Numer. Math. 15 (1970), 283 - 296. (1970) MR0275014DOI10.1007/BF02165119

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