Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the L p -space

Marián Slodička

Aplikace matematiky (1989)

  • Volume: 34, Issue: 6, page 439-448
  • ISSN: 0862-7940

Abstract

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The Rothe-Galerkin method is used for discretization. The rate of convergence in C ( I , L p ( G ) ) for the approximate solution of a quasilinear parabolic equation with a Volterra operator on the right-hand side is established.

How to cite

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Slodička, Marián. "Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_p$-space." Aplikace matematiky 34.6 (1989): 439-448. <http://eudml.org/doc/15599>.

@article{Slodička1989,
abstract = {The Rothe-Galerkin method is used for discretization. The rate of convergence in $C(I, L_p(G))$ for the approximate solution of a quasilinear parabolic equation with a Volterra operator on the right-hand side is established.},
author = {Slodička, Marián},
journal = {Aplikace matematiky},
keywords = {error estimate; Rothe’s method; semidiscretization in time; quasilinear parabolic Volterra integro-differential equation; rate of convergence; galerkin's method; error estimate; Rothe's method; semidiscretization in time; quasilinear parabolic Volterra integro-differential equation; rate of convergence},
language = {eng},
number = {6},
pages = {439-448},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_p$-space},
url = {http://eudml.org/doc/15599},
volume = {34},
year = {1989},
}

TY - JOUR
AU - Slodička, Marián
TI - Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_p$-space
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 6
SP - 439
EP - 448
AB - The Rothe-Galerkin method is used for discretization. The rate of convergence in $C(I, L_p(G))$ for the approximate solution of a quasilinear parabolic equation with a Volterra operator on the right-hand side is established.
LA - eng
KW - error estimate; Rothe’s method; semidiscretization in time; quasilinear parabolic Volterra integro-differential equation; rate of convergence; galerkin's method; error estimate; Rothe's method; semidiscretization in time; quasilinear parabolic Volterra integro-differential equation; rate of convergence
UR - http://eudml.org/doc/15599
ER -

References

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  2. J. Descloux, Basic properties of Sobolev spaces, approximation by finite elements, Ecole polytechnique féderale Lausanne, Switzerland 1975. (1975) 
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  6. J. Kačur, Application of Rothe's method to evolution integrodifferential equations, Universität Heidelberg, SFB 123, 381, 1986. (1986) Zbl0638.65098
  7. J. Kačur, Method or Rothe in evolution equations, Teubner Texte zur Mathematik 80, Leipzig 1985. (1985) Zbl0582.65084MR0834176
  8. A. Kufner O. John S. Fučík, Function spaces, Academia, Prague 1977. (1977) Zbl0364.46022MR0482102
  9. M. Marino A. Maugeri, 10.1007/BF01766852, Ann. Mat. Рurа Appl. 139 (1985), 107-145. (1985) Zbl0576.35063MR0798171DOI10.1007/BF01766852
  10. V. Pluschke, Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method, (to appear in Czechoslovak. Math. J.). Zbl0671.35037MR0962908
  11. K. Rektorys, The method of discretization in time and and partial differential equations, D. Reidel. Publ. Do., Dordrecht-Boston-London 1982. (1982) Zbl0522.65059MR0689712
  12. Ch. G. Simander, On Dirichlet's boundary value problem, Lecture Notes in Math. 268, Springer-Verlag, Berlin-Heidelberg-New York 1972. (1972) 
  13. M. Slodička, An investigation of convergence and error estimate of approximate solution for quasiliriear integrodifferential equation, (to appear). Zbl0725.65138
  14. W. von Wahl, 10.1112/jlms/s2-25.3.483, J. London Math. Soc. 25 (1982), 483 - 497. (1982) Zbl0493.35050MR0657505DOI10.1112/jlms/s2-25.3.483
  15. V. Thomee, Galerkin finite element method 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

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