Finite element discretization of the Kuramoto-Sivashinsky equation

Georgios Akrivis

Banach Center Publications (1994)

  • Volume: 29, Issue: 1, page 155-163
  • ISSN: 0137-6934

Abstract

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We analyze semidiscrete and second-order in time fully discrete finite element methods for the Kuramoto-Sivashinsky equation.

How to cite

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Akrivis, Georgios. "Finite element discretization of the Kuramoto-Sivashinsky equation." Banach Center Publications 29.1 (1994): 155-163. <http://eudml.org/doc/262830>.

@article{Akrivis1994,
abstract = {We analyze semidiscrete and second-order in time fully discrete finite element methods for the Kuramoto-Sivashinsky equation.},
author = {Akrivis, Georgios},
journal = {Banach Center Publications},
keywords = {Kuramoto-Sivashinsky equation; semidiscrete method; finite element method; Galerkin method; Crank-Nicolson scheme; error estimate},
language = {eng},
number = {1},
pages = {155-163},
title = {Finite element discretization of the Kuramoto-Sivashinsky equation},
url = {http://eudml.org/doc/262830},
volume = {29},
year = {1994},
}

TY - JOUR
AU - Akrivis, Georgios
TI - Finite element discretization of the Kuramoto-Sivashinsky equation
JO - Banach Center Publications
PY - 1994
VL - 29
IS - 1
SP - 155
EP - 163
AB - We analyze semidiscrete and second-order in time fully discrete finite element methods for the Kuramoto-Sivashinsky equation.
LA - eng
KW - Kuramoto-Sivashinsky equation; semidiscrete method; finite element method; Galerkin method; Crank-Nicolson scheme; error estimate
UR - http://eudml.org/doc/262830
ER -

References

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  1. [1] G. D. Akrivis, Finite difference discretization of the Kuramoto-Sivashinsky equation, Numer. Math. 63 (1992), 1-11. Zbl0762.65071
  2. [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. [3] P. Constantin, C. Foiaş, B. Nicolaenko and R. Temam, Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Springer, New York 1989. Zbl0683.58002
  4. [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. Zbl0602.58033
  5. [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. Zbl0704.58030
  6. [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. Zbl0722.35011
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  9. [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. Zbl0592.35013
  10. [10] J. Nitsche, Umkehrsätze für Spline-Approximationen, Compositio Math. 21 (1969), 400-416. Zbl0199.39302
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  12. [12] R. Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1182-1238. Zbl0411.52006
  13. [13] D. T. Papageorgiou, C. Maldarelli and D. S. Rumschitzki, Nonlinear interfacial stability of core-annular film flows, Phys. Fluids A2 (1990), 340-352. Zbl0704.76060
  14. [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. Zbl0728.76055
  15. [15] L. L. Schumaker, Spline Functions: Basic Theory, Wiley, New York 1981. Zbl0449.41004
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  17. [17] E. Tadmor, The well-posedness of the Kuramoto-Sivashinsky equation, SIAM J. Math. Anal. 17 (1986), 884-893. Zbl0606.35073
  18. [18] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Sprin- ger, New York 1988. 

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