About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

First Page Preview
Hlaváček, Ivan
Domain optimization in axisymmetric elliptic boundary value problems by finite elements. (English). Aplikace matematiky, vol. 33 (1988), issue 3, pp. 213-244
MSC: 35J25, 49A22, 65K10, 65N30, 65N99 | MR 0944785 | Zbl 0677.65102 | DOI: 10.21136/AM.1988.104304
Keywords:
domain optimization; triangular finite element spaces; cost functionals
Summary:
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces.
References:
[1] D. Begis R. Glowinski: Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Appl. Math. & Optim. 2 (1975), 130-169. DOI 10.1007/BF01447854 | MR 0443372
[2] B. Mercier G. Raugel: Résolution d'un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et series de Fourier en $\theta$. R. A. I. R. O. , Anal. numér., 16 (1982), 405-461. MR 0684832
[3] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. MR 0227584
[4] H. Triebel: Interpolation Theory, Function Spaces, Differential Operators. DVW, Berlin 1978. MR 0503903 | Zbl 0387.46033
[5] P. G. Ciarlet: The finite element method for elliptic problems. North- Holland, Amsterdam 1978. MR 0520174 | Zbl 0383.65058
Partner of
EuDML logo