Article
MSC:
35K22,
45G10,
45K05,
45L05,
45N05,
65M15,
65M20,
65R20 | MR 1039408 | Zbl 0725.65138 | DOI: 10.21136/AM.1990.104384
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Keywords:
Rothe's method; Galerkin's method; error estimates; convergence; quasilinear parabolic integrodifferential problem; abstract real Hilbert space
Rothe's method; Galerkin's method; error estimates; convergence; quasilinear parabolic integrodifferential problem; abstract real Hilbert space
Summary:
One parabolic integrodifferential problem in the abstract real Hilbert spaces is studied in this paper. The semidiscrete and full discrete approximate solution is defined and the error estimate of Rothe's function in some function spaces is established.
References:
[1] P. G. Ciarlet: The finite element method for elliptic problems. North Holland, Amsterdam 1978. MR 0520174 | Zbl 0383.65058
[2] J. Douglas T. Dupont M. F. Wheeler: A quasi-projection analysis of Galerkin methods for parabolic and hyperbolic equations. Math. Соmр. 32 (1978), 345-362. MR 0495012
[3] R. Glowinski J. L. Lions R. Tremolieres: Analyse numerique des inequations variationelles. Dunod, Paris 1976.
[4] J. Kačur: Application of Rothe's method to evolution integrodifferential equations. J. reine angew. Math. 388 (1988), 73-105. MR 0944184 | Zbl 0638.65098
[5] J. Kačur: Method of Rothe in evolution equations. Teubner Texte zur Mathematik 80, Leipzig 1985. MR 0834176
[6] J. Kačur A. Ženíšek: Analysis of approximate solutions of coupled dynamical thermoelasticity and related problems. Apl. mat. 31 (1986), 190-223. MR 0837733
[7] A. Kufner O. John S. Fučík: Function spaces. Academia, Prague 1977. MR 0482102
[8] J. T. Oden J. N. Reddy: An introduction to the mathematical theory of finite elements. J. Wiley & sons, New York- London- Sydney 1976. MR 0461950
[9] V. Pluschke: Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method. (to appear in Czech. Math. J.). MR 0962908 | Zbl 0671.35037
[10] K. Rektorys : The method of discretization in time and partial differential equations. D. Reidel Publ. Co., Dordrecht - Boston- London 1982. MR 0689712 | Zbl 0522.65059
[11] А. А. Самарский: Теория разностных схем. Наука. Москва 1977. Zbl 1155.81371
[12] M. Slodička: Application of Rothe's method to evolution integrodifferential systems. CMUC 30, 1 (1989), 57-70. MR 0995701 | Zbl 0674.65110
[13] M. Slodička: О слабом решении одной системы квазилинейных интегродифференциальных эволюционных уравнений. ОИЯИ. Р5-87-765, Дубна 1987.
[14] G. Strong G. J. Fix: An analysis of the finite element method. Prentice-Hall, Englewood Cliffs, N. J. 1973. MR 0443377
[15] V. Thomee: Galerkin finite element methods for parabolic problems. Lecture Notes in Math. 1054, Springer-Verlag, Berlin- Heidelberg- New York- Tokyo 1984. MR 0744045 | Zbl 0528.65052
[16] M. F. Wheeler: A priori $L_2$-error estimates for Galerkin approximations to parabolic partial differential equations. SIAM J. Numer. Anal. 10 (1973), 723 - 759. DOI 10.1137/0710062 | MR 0351124
[17] M. Zlámal: A linear scheme for the numerical solution of nonlinear quasistationary magnetic fields. Math. of Соmр. 41 (1983), 425-440. MR 0717694
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