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1994 | 29 | 1 | 165-173
Tytuł artykułu

Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.
Rocznik
Tom
29
Numer
1
Strony
165-173
Opis fizyczny
Daty
wydano
1994
Twórcy
  • University of Belgrade, Faculty of Sciences, Studentski trg 16, POB 550, 11000 Belgrade, Yugoslavia
Bibliografia
  • [1] R. A. Adams, Sobolev Spaces, Academic Press, New York 1975.
  • [2] J. H. Bramble and S. R. Hilbert, Bounds for a class of linear functionals with application to Hermite interpolation, Numer. Math. 16 (1971), 362-369.
  • [3] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam 1978.
  • [4] T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34 (1980), 441-463.
  • [5] B. S. Jovanović, On the convergence of finite-difference schemes for parabolic equations with variable coefficients, Numer. Math. 54 (1989), 395-404.
  • [6] B. S. Jovanović, Optimal error estimates for finite-difference schemes with variable coefficients, Z. Angew. Math. Mech. 70 (1990), 640-642.
  • [7] B. S. Jovanović, Convergence of finite-difference schemes for parabolic equations with variable coefficients, ibid. 71 (1991), 647-650.
  • [8] B. S. Jovanović, Convergence of finite-difference schemes for hyperbolic equations with variable coefficients, ibid. 72 (1992), to appear.
  • [9] B. S. Jovanović, L. D. Ivanović and E. E. Süli, Convergence of a finite-difference scheme for second-order hyperbolic equations with variable coefficients, IMA J. Numer. Anal. 7 (1987), 39-45.
  • [10] B. S. Jovanović, L. D. Ivanović and E. E. Süli, Convergence of finite-difference schemes for elliptic equations with variable coefficients, ibid., 301-305.
  • [11] R. D. Lazarov, On the question of convergence of finite-difference schemes for generalized solutions of the Poisson equation, Differentsial'nye Uravneniya 17 (1981), 1285-1294 (in Russian).
  • [12] R. D. Lazarov, V. L. Makarov and A. A. Samarskiĭ, Application of exact difference schemes for construction and investigation of difference schemes for generalized solutions, Mat. Sb. 117 (1982), 469-480 (in Russian).
  • [13] R. D. Lazarov, V. L. Makarov and W. Weinelt, On the convergence of difference schemes for the approximation of solutions $u ∈ W_2^m$ (m > 0.5) of elliptic equations with mixed derivatives, Numer. Math. 44 (1984), 223-232.
  • [14] V. G. Maz'ya and T. O. Shaposhnikova, Theory of Multipliers in Spaces of Differentiable Functions, Monographs Stud. Math. 23, Pitman, Boston 1985.
  • [15] A. A. Samarskiĭ, Theory of Difference Schemes, Nauka, Moscow 1983 (in Russian).
  • [16] E. Süli, B. Jovanović and L. Ivanović, Finite difference approximations of generalized solutions, Math. Comp. 45 (1985), 319-327.
  • [17] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag der Wissenschaften, Berlin 1978.
  • [18] J. Wloka, Partial Differential Equations, Cambridge Univ. Press, 1987.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv29z1p165bwm
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