Finite element discretization of the Kuramoto-Sivashinsky equation
Akrivis, Georgios
Banach Center Publications, Tome 29 (1994), p. 155-163 / Harvested from The Polish Digital Mathematics Library
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We analyze semidiscrete and second-order in time fully discrete finite element methods for the Kuramoto-Sivashinsky equation.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:262830 
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     author = {Akrivis, Georgios},
     title = {Finite element discretization of the Kuramoto-Sivashinsky equation},
     journal = {Banach Center Publications},
     volume = {29},
     year = {1994},
     pages = {155-163},
     zbl = {0804.65119},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv29z1p155bwm}
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Akrivis, Georgios. Finite element discretization of the Kuramoto-Sivashinsky equation. Banach Center Publications, Tome 29 (1994) pp. 155-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv29z1p155bwm/

[000] [1] G. D. Akrivis, Finite difference discretization of the Kuramoto-Sivashinsky equation, Numer. Math. 63 (1992), 1-11. | Zbl 0762.65071

[001] [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.

[002] [3] P. Constantin, C. Foiaş, B. Nicolaenko and R. Temam, Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Springer, New York 1989. | Zbl 0683.58002

[003] [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. | Zbl 0602.58033

[004] [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. | Zbl 0704.58030

[005] [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. | Zbl 0722.35011

[006] [7] Y. Kuramoto, Diffusion induced chaos in reaction systems, Progr. Theoret. Phys. Suppl. 64 (1978), 346-367.

[007] [8] B. Nicolaenko and B. Scheurer, Remarks on the Kuramoto-Sivashinsky equation, Phys. D 12 (1984), 391-395. | Zbl 0576.35058

[008] [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. | Zbl 0592.35013

[009] [10] J. Nitsche, Umkehrsätze für Spline-Approximationen, Compositio Math. 21 (1969), 400-416. | Zbl 0199.39302

[010] [11] J. Nitsche, Verfahren von Ritz und Spline-Interpolation bei Sturm-Liouville-Randwertproblemen, Numer. Math. 13 (1969), 260-265. | Zbl 0181.18204

[011] [12] R. Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1182-1238. | Zbl 0411.52006

[012] [13] D. T. Papageorgiou, C. Maldarelli and D. S. Rumschitzki, Nonlinear interfacial stability of core-annular film flows, Phys. Fluids A2 (1990), 340-352. | Zbl 0704.76060

[013] [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. | Zbl 0728.76055

[014] [15] L. L. Schumaker, Spline Functions: Basic Theory, Wiley, New York 1981. | Zbl 0449.41004

[015] [16] G. I. Sivashinsky, On flame propagation under conditions of stoichiometry, SIAM J. Appl. Math. 39 (1980), 67-82. | Zbl 0464.76055

[016] [17] E. Tadmor, The well-posedness of the Kuramoto-Sivashinsky equation, SIAM J. Math. Anal. 17 (1986), 884-893. | Zbl 0606.35073

[017] [18] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Sprin- ger, New York 1988.