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1994 | 29 | 1 | 155-163
Tytuł artykułu

Finite element discretization of the Kuramoto-Sivashinsky equation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We analyze semidiscrete and second-order in time fully discrete finite element methods for the Kuramoto-Sivashinsky equation.
Słowa kluczowe
Rocznik
Tom
29
Numer
1
Strony
155-163
Opis fizyczny
Daty
wydano
1994
Twórcy
  • Mathematics Department, University of Crete, 71409 Heraklion, Greece
Bibliografia
  • [1] G. D. Akrivis, Finite difference discretization of the Kuramoto-Sivashinsky equation, Numer. Math. 63 (1992), 1-11.
  • [2] F. E. Browder, Existence and uniqueness theorems for solutions of nonlinear boundary value problems, in: Applications of Nonlinear Partial Differential Equations, R. Finn (ed.), Proc. Sympos. Appl. Math. 17, Amer. Math. Soc., Providence 1965, 24-49.
  • [3] P. Constantin, C. Foiaş, B. Nicolaenko and R. Temam, Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Springer, New York 1989.
  • [4] J. M. Hyman and B. Nicolaenko, The Kuramoto-Sivashinsky equation: A bridge between PDE's and dynamical systems, Phys. D 18 (1986), 113-126.
  • [5] J. M. Jolly, I. G. Kevrekidis and E. S. Titi, Approximate inertial manifolds for the Kuramoto-Sivashinsky equation; analysis and computations, ibid. 44 (1990), 38-60.
  • [6] I. G. Kevrekidis, B. Nicolaenko and J. C. Scovel, Back in the saddle again; a computer assisted study of the Kuramoto-Sivashinsky equation, SIAM J. Appl. Math. 50 (1990), 760-790.
  • [7] Y. Kuramoto, Diffusion induced chaos in reaction systems, Progr. Theoret. Phys. Suppl. 64 (1978), 346-367.
  • [8] B. Nicolaenko and B. Scheurer, Remarks on the Kuramoto-Sivashinsky equation, Phys. D 12 (1984), 391-395.
  • [9] B. Nicolaenko, B. Scheurer and R. Temam, Some global dynamical properties of the Kuramoto-Sivashinsky equation: Nonlinear stability and attractors, ibid. 16 (1985), 155-183.
  • [10] J. Nitsche, Umkehrsätze für Spline-Approximationen, Compositio Math. 21 (1969), 400-416.
  • [11] J. Nitsche, Verfahren von Ritz und Spline-Interpolation bei Sturm-Liouville-Randwertproblemen, Numer. Math. 13 (1969), 260-265.
  • [12] R. Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1182-1238.
  • [13] D. T. Papageorgiou, C. Maldarelli and D. S. Rumschitzki, Nonlinear interfacial stability of core-annular film flows, Phys. Fluids A2 (1990), 340-352.
  • [14] D. T. Papageorgiou and Y. S. Smyrlis, The route to chaos for the Kuramoto-Sivashin- sky equation, Theoret. Comput. Fluid Dynamics 3 (1991), 15-42.
  • [15] L. L. Schumaker, Spline Functions: Basic Theory, Wiley, New York 1981.
  • [16] G. I. Sivashinsky, On flame propagation under conditions of stoichiometry, SIAM J. Appl. Math. 39 (1980), 67-82.
  • [17] E. Tadmor, The well-posedness of the Kuramoto-Sivashinsky equation, SIAM J. Math. Anal. 17 (1986), 884-893.
  • [18] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Sprin- ger, New York 1988.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv29z1p155bwm
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