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Special exact curved finite elements. (English) Zbl 0760.65008
The author describes a type of curved elements suitable for solving contact problems of the second order in domains \(\Omega\) whose boundaries \(\Gamma\) consist of a finite number of circular arcs and a finite number of line segments. The suggested curved elements, so-called special exact curved finite elements, can be used not only along the boundary \(\Gamma\) but also in the interior of \(\Omega\) and are the natural generalizations of linear elements in the case of boundaries \(\Gamma\) described above.

65D15 Algorithms for approximation of functions
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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[1] J. Křižková O. Blahník: Application of Special Curved Elements to the Solution of the Electromagnetic Field. Applied Mathematics Notes, vol. 14 (1989), 8-25.
[2] L. Holuša A. Ženíšek: Applications of Curved Triangular Finite \(C^1\) - Elements. Proceedings of Algorithms 79, Vysoké Tatry 1979, 128-136.
[3] V. Kolář J. Kratochvíl F. Leitner A. Ženíšek: Computation of Surface and Space Constructions by the Finite Element Method. (Czech). Praha, SNTL 1979.
[4] A. Kufner O. John S. Fučík: Function Spaces. Academia, Praha 1977.
[5] J. Nečas: Les méthodes directes en théorie des equations elliptiques. Academia, Praha 1967. · Zbl 1225.35003
[6] K. Rektorys: Variační metody v inženýrských problémech a problémech matematické fyziky. Praha SNTL 1979.
[7] M. Zlámal: On the Finite Element Method. Numer. Math. 12 (1968), 394-409. · Zbl 0176.16001
[8] M. Zlámal: Curved Elements in the Finite Element Method I. SIAM J. Numer. Anal. vol. 10. No 1 (1973), 229-240. · Zbl 0285.65067 · doi:10.1137/0710022
[9] M. Zlámal: Curved Elements in the Finite Element Method II. SIAM J. Numer. Anal. vol. 11. No 2 (1974), 347-462.
[10] A. Ženíšek: Interpolation Polynomials on the Triangle. Numer. Math. 15 (1970), 283-296. · Zbl 0216.38901
[11] A. Ženíšek: Curved Triangular Finite \(C^m\)-Elements. Aplikace matematiky 23 (1978), 346-377. · Zbl 0404.35041
[12] A. Ženíšek: Curved Triangular \(C^m\)-Elements and their Applications. (Czech), Sborník referátů III. letní školy Software a algoritmy numer. mat., Nové Město na Moravě 1979.
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