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Keywords:
finite element method; nonlipschitz boundary; cusp points (turning points); maximum angle condition; minimum angle condition; linear elliptic problems
finite element method; nonlipschitz boundary; cusp points (turning points); maximum angle condition; minimum angle condition; linear elliptic problems
Summary:
The finite element analysis of linear elliptic problems in two-dimensional domains with cusp points (turning points) is presented. This analysis needs on one side a generalization of results concerning the existence and uniqueness of the solution of a constinuous elliptic variational problem in a domain the boundary of which is Lipschitz continuous and on the other side a presentation of a new finite element interpolation theorem and other new devices.
References:
[1] P. Doktor: On the density of smooth functions in certain subspaces of Sobolev Space. CMUC 14 (1973), 609-622. MR 0336317 | Zbl 0268.46036
[2] M. Feistauer, and A. Ženíšek: Finite element solution of nonlinear elliptic problems. Numer. Math. 50 (1987), 451-475. DOI 10.1007/BF01396664 | MR 0875168
[3] A. Kufner: Boundary value problems in weighted spaces. Equadiff 6, Proceedings of the International Conference on Differential Equations and their Applications held in Brno, Czechoslovakia, August 1985 (J. Vosmanský and M. Zlámal, eds.), Springer- Verlag, Berlin, 1986, pp. 35-48. MR 0877105
[4] A. Kufner O. John, and S. Fučík: Function Spaces. Academia, Prague, 1977. MR 0482102
[5] J. Nečas: Les Méthodes Directes en Théorie des Equations Elliptiques. Academia, Prague, 1967. MR 0227584
[6] L. A. Oganesian, and L. A. Rukhovec: Variational Difference Methods for the Solution of Elliptic Problems. Izd. Akad. Nauk ArSSR, Jerevan, 1979. (In Russian.)
[7] J. L. Synge: The Hypercircle in Mathematical Physics. Cambridge University Press, Cambridge, 1957. MR 0097605 | Zbl 0079.13802
[8] A. Ženíšek: Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations. Academic Press, London, 1990. MR 1086876
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