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1994 | 29 | 1 | 135-154
Tytuł artykułu

Finite differences and boundary element methods for non-stationary viscous incompressible flow

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is carried out.
Słowa kluczowe
Rocznik
Tom
29
Numer
1
Strony
135-154
Opis fizyczny
Daty
wydano
1994
Twórcy
  • Technical University of Dresden, Institute of Numerical Mathematics, 01062 Dresden, Germany
Bibliografia
  • [
  • [1] W. Borchers, Über das Anfangsrandwertproblem der instationären Stokes Gleichung, Z. Angew. Math. Mech. 65 (1985), T329-T330.
  • [2] L. Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Sem. Mat. Univ. Padova 31 (1964), 308-340.
  • [3] M. Costabel, Principles of boundary element methods, preprint 998, Technische Hochschule Darmstadt, 1986.
  • [4] P. Deuring, W. von Wahl and P. Weidemaier, Das lineare Stokes-System im ℝ³ (1. Vorlesungen über das Innenraumproblem), Bayreuth. Math. Schr. 27 (1988), 1-252.
  • [5] H. Fujita and T. Kato, On the Navier-Stokes initial value problem I, Arch. Rational Mech. Anal. 16 (1964), 269-315.
  • [6] F. K. Hebeker, Efficient boundary element methods for three-dimensional exterior viscous flow, Numer. Methods Partial Differential Equations 2 (1986), 273-297.
  • [7] G. C. Hsiao, P. Kopp and W. L. Wendland, A Galerkin collocation method for some integral equations of the first kind, Computing 25 (1980), 89-130.
  • [8] G. C. Hsiao, P. Kopp and W. L. Wendland, Some applications of a Galerkin-collocation method for boundary integral equations of the first kind, Math. Methods Appl. Sci. 6 (1984), 280-325.
  • [9] J. Kačur, Method of Rothe in Evolution Equations, Teubner-Texte Math. 80, Teubner, Leipzig 1985.
  • [10] O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York 1969.
  • [11] P. D. Lax and R. D. Richtmyer, Survey of the stability of linear finite difference equations, Comm. Pure Appl. Math. 9 (1956), 267-293.
  • [12] R. Leis, Vorlesungen über partielle Differentialgleichungen zweiter Ordnung, Bibliographisches Institut, Mannheim 1967.
  • [13] M. Mc Cracken, The resolvent problem for the Stokes equations on halfspace in $L_p$, SIAM J. Math. Anal. 12 (1981), 201-228.
  • [14] F. K. G. Odquist, Über die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten, Math. Z. 32 (1930), 329-375.
  • [15] W. I. Smirnow, Lehrgang der höheren Mathematik 4, Deutscher Verlag der Wissenschaften, Berlin 1979.
  • [16] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam 1977.
  • [17] W. Varnhorn, Efficient quadrature for a boundary element method to compute threedimensional Stokes flow, Internat. J. Numer. Methods Fluids 9 (1989), 185-191.
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Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv29z1p135bwm
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