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error estimate; Rothe’s method; semidiscretization in time; quasilinear parabolic Volterra integro-differential equation; rate of convergence; galerkin's method
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.
[1] P. G. Ciarlet: The finite element method for elliptic problems. North. Holland, Amsterdam 1978. MR 0520174 | Zbl 0383.65058
[2] J. Descloux: Basic properties of Sobolev spaces, approximation by finite elements. Ecole polytechnique féderale Lausanne, Switzerland 1975.
[3] G. Di Blasio: Linear parabolic evolution equations in $L_p$-spaces. Ann. Mat. Рurа Appl. 138 (1984), 55-104. DOI 10.1007/BF01762539 | MR 0779538
[4] R. Glowinski J. L. Lions R. Tremolieres: Analyse numerique des inequations variationelles. Dunod, Paris 1976.
[5] D. Henry: Geometric theory of semilinear parabolic equations. Springer-Verlag, Berlin - Heidelberg-New York 1981. MR 0610244 | Zbl 0456.35001
[6] J. Kačur: Application of Rothe's method to evolution integrodifferential equations. Universität Heidelberg, SFB 123, 381, 1986.
[7] J. Kačur: Method or Rothe in evolution equations. Teubner Texte zur Mathematik 80, Leipzig 1985. MR 0834176
[8] A. Kufner O. John S. Fučík: Function spaces. Academia, Prague 1977. MR 0482102
[9] M. Marino A. Maugeri: $L_p$-theory and partial Hölder continuity for quasilinear parabolic systems of higher order with strictly controlled growth. Ann. Mat. Рurа Appl. 139 (1985), 107-145. DOI 10.1007/BF01766852 | MR 0798171
[10] V. Pluschke: Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method. (to appear in Czechoslovak. Math. J.). MR 0962908 | Zbl 0671.35037
[11] K. Rektorys: The method of discretization in time and and partial differential equations. D. Reidel. Publ. Do., Dordrecht-Boston-London 1982. MR 0689712
[12] Ch. G. Simander: On Dirichlet's boundary value problem. Lecture Notes in Math. 268, Springer-Verlag, Berlin-Heidelberg-New York 1972.
[13] M. Slodička: An investigation of convergence and error estimate of approximate solution for quasiliriear integrodifferential equation. (to appear).
[14] W. von Wahl: The equation $u' + A(t) u = f$ in a Hilbert space and $L_p$-estimates for parabolic equations. J. London Math. Soc. 25 (1982), 483 - 497. DOI 10.1112/jlms/s2-25.3.483 | MR 0657505 | Zbl 0493.35050
[15] V. Thomee: Galerkin finite element method for parabolic problems. Lecture Notes in Math. 1054, Springer-Verlag, Berlin -Heidelberg-New York-Tokyo 1984. MR 0744045
[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
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