Abstract
New classes of problems with discontinuous solutions are considered. Corresponding generalized problems are obtained. Increased-accuracy computational schemes for their discretization are proposed. Numerical schemes are proposed with asymptotic accuracy not worse than that of similar schemes for problems with smooth solutions.
Similar content being viewed by others
References
I. V. Sergienko and V. S. Deineka, “Problems with conjugation conditions and their high-accuracy computational discretization algorithms,” Kibern. Sist. Anal., No. 6, 100-124 (1999).
V. S. Deineka, I. V. Sergienko, and V. V. Skopetskii, Models and Methods of Solution of Problems with Conjugation Conditions [in Russian], Naukova Dumka, Kiev (1998).
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1972).
A. Baker Garth, “Error estimates for finite element methods for second-order hyperbolic equations,” SIAM J. Numer. Anal.,13, No. 4, 564–576 (1976).
I. S. Berezin and N. T. Zhidkov, Methods of Calculations [in Russian], Vol 2, Fizmatgiz, Moscow (1972).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).
S. P. Timoshenko, A Course of the Theory of Elasticity [in Russian], Naukova Dumka, Kiev (1972).
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 system of elliptic equations,” Applicace Matematiky,14, No. 5, 39–45 (1969).
Author information
Authors and Affiliations
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 110–131, January–February, 2000.
Rights and permissions
About this article
Cite this article
Sergienko, I.V., Deineka, V.S. Models with conjugation conditions and high-accuracy methods of their discretization. Cybern Syst Anal 36, 83–101 (2000). https://doi.org/10.1007/BF02733304
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02733304