Abstract
We consider new eigenvalue problems with discontinuous eigenfunctions and construct computational algorithms whose accuracy is not worse than the accuracy of analogous known algorithms for problems with smooth eigenfunctions.
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References
V.S. Zarubin,Engineering Methods for the Solution of Problems of Heat Conduction [in Russian], Énergoatomizdat, Moscow (1983).
Yu. P. Shlykov and E. A. Ganin,Contact Heat Transfer [in Russian], Énergoatomizdat, Moscow-Leningrad (1987).
L.A. Kozdoba,Methods for the Solution of Nonlinear Problems of Heat Conduction [in Russian], Naukova Dumka, Kiev (1975).
I.V. Sergienko, V. V. Skopetskii, and V. S. Deineka,Mathematical Simulation and Investigation of Processes in Inhomogeneous Media [in Russian], Naukova Dumka, Kiev (1991).
W.G. Strang and G. J. Fix,An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ (1973).
S.G. Mikhlin,Variational Methods in Mathematical Physics [in Russian], Mir, Moscow (1970).
V.S. Deineka, I. V. Sergienko, and V. V. Skopetskii,Mathematical Models and Methods for the Calculation of Problems with Discontinuous Solutions [in Russian], Naukova Dumka, Kiev (1995).
M. Zlamal, “On the finite element method,”Numer. Math.,12, No. 5, 393–409 (1968).
A. Zenisek, “Convergence of a finite element procedure for solving boundary-value problems of the systems of elliptic equations,”Appl. Math.,14, No. 5, 39–45 (1969).
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Institute of Cybernetics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 10, pp. 1317–1323, October, 1999.
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Deineka, V.S., Sergienko, I.V. & Skopetskii, V.V. Eigenvalue problems with discontinuous eigenfunctions and their numerical solutions. Ukr Math J 51, 1484–1492 (1999). https://doi.org/10.1007/BF02981681
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DOI: https://doi.org/10.1007/BF02981681