An investigation of convergence and error estimate of approximate solution for a quasilinear parabolic integrodifferential equation

Marián Slodička

Aplikace matematiky (1990)

  • Volume: 35, Issue: 1, page 16-27
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Slodička, Marián. "An investigation of convergence and error estimate of approximate solution for a quasilinear parabolic integrodifferential equation." Aplikace matematiky 35.1 (1990): 16-27. <http://eudml.org/doc/15607>.

@article{Slodička1990,
abstract = {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.},
author = {Slodička, Marián},
journal = {Aplikace matematiky},
keywords = {Rothe's method; Galerkin's method; error estimates; convergence; quasilinear parabolic integrodifferential problem; abstract real Hilbert space; Rothe's method; convergence; quasilinear parabolic integrodifferential problem; abstract real Hilbert space; error estimates},
language = {eng},
number = {1},
pages = {16-27},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An investigation of convergence and error estimate of approximate solution for a quasilinear parabolic integrodifferential equation},
url = {http://eudml.org/doc/15607},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Slodička, Marián
TI - An investigation of convergence and error estimate of approximate solution for a quasilinear parabolic integrodifferential equation
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 1
SP - 16
EP - 27
AB - 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.
LA - eng
KW - Rothe's method; Galerkin's method; error estimates; convergence; quasilinear parabolic integrodifferential problem; abstract real Hilbert space; Rothe's method; convergence; quasilinear parabolic integrodifferential problem; abstract real Hilbert space; error estimates
UR - http://eudml.org/doc/15607
ER -

References

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  1. P. G. Ciarlet, The finite element method for elliptic problems, North Holland, Amsterdam 1978. (1978) Zbl0383.65058MR0520174
  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. (1978) Zbl0385.65052MR0495012
  3. R. Glowinski J. L. Lions R. Tremolieres, Analyse numerique des inequations variationelles, Dunod, Paris 1976. (1976) Zbl0358.65091
  4. J. Kačur, Application of Rothe's method to evolution integrodifferential equations, J. reine angew. Math. 388 (1988), 73-105. (1988) Zbl0638.65098MR0944184
  5. J. Kačur, Method of Rothe in evolution equations, Teubner Texte zur Mathematik 80, Leipzig 1985. (1985) Zbl0582.65084MR0834176
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  9. V. Pluschke, Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method, (to appear in Czech. Math. J.). Zbl0671.35037MR0962908
  10. K. Rektorys, The method of discretization in time and partial differential equations, D. Reidel Publ. Co., Dordrecht - Boston- London 1982. (1982) Zbl0522.65059MR0689712
  11. А. А. Самарский, Теория разностных схем, Наука. Москва 1977. (1977) Zbl1155.81371
  12. M. Slodička, Application of Rothe's method to evolution integrodifferential systems, CMUC 30, 1 (1989), 57-70. (1989) Zbl0674.65110MR0995701
  13. M. Slodička, О слабом решении одной системы квазилинейных интегродифференциальных эволюционных уравнений, ОИЯИ. Р5-87-765, Дубна 1987. (1987) 
  14. G. Strong G. J. Fix, An analysis of the finite element method, Prentice-Hall, Englewood Cliffs, N. J. 1973. (1973) MR0443377
  15. V. Thomee, Galerkin finite element methods for parabolic problems, Lecture Notes in Math. 1054, Springer-Verlag, Berlin- Heidelberg- New York- Tokyo 1984. (1984) Zbl0528.65052MR0744045
  16. M. F. Wheeler, 10.1137/0710062, SIAM J. Numer. Anal. 10 (1973), 723 - 759. (1973) MR0351124DOI10.1137/0710062
  17. M. Zlámal, A linear scheme for the numerical solution of nonlinear quasistationary magnetic fields, Math. of Соmр. 41 (1983), 425-440. (1983) MR0717694

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