High-order finite element methods for the Kuramoto-Sivashinsky equation
ESAIM: Modélisation mathématique et analyse numérique, Tome 30 (1996) no. 2, pp. 157-183. 
@article{M2AN_1996__30_2_157_0,
     author = {Akrivis, Georgios},
     title = {High-order finite element methods for the {Kuramoto-Sivashinsky} equation},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {157--183},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {30},
     number = {2},
     year = {1996},
     mrnumber = {1382109},
     zbl = {0842.76035},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1996__30_2_157_0/}
}
TY  - JOUR
AU  - Akrivis, Georgios
TI  - High-order finite element methods for the Kuramoto-Sivashinsky equation
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1996
SP  - 157
EP  - 183
VL  - 30
IS  - 2
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1996__30_2_157_0/
LA  - en
ID  - M2AN_1996__30_2_157_0
ER  - 
%0 Journal Article
%A Akrivis, Georgios
%T High-order finite element methods for the Kuramoto-Sivashinsky equation
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1996
%P 157-183
%V 30
%N 2
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1996__30_2_157_0/
%G en
%F M2AN_1996__30_2_157_0
Akrivis, Georgios. High-order finite element methods for the Kuramoto-Sivashinsky equation. ESAIM: Modélisation mathématique et analyse numérique, Tome 30 (1996) no. 2, pp. 157-183. http://www.numdam.org/item/M2AN_1996__30_2_157_0/

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

[2] G. D. Akrivis, 1994, Finite element discretization of the Kuramoto-Sivashinsky equation. Banach Center Publications, 29, pp. 155-163. | MR | Zbl

[3] G. Akrivis, V. A. Dougalis, O. Karakashian, Solving the Systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods. Submitted. | Numdam | Zbl

[4] J. H. Bramble, P. H. Sammon, 1980, Efficient higher order single step methods for parabolic problems. Part I, Math. Comp., 35, pp. 655-677. | MR | Zbl

[5] P. Constantin, C. Foias, B. Nicolaenko, R. Temam, 1989, Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, New York, Springer-Verlag. | MR | Zbl

[6] K. Dekker, J. G. Verwer, 1984, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, Amsterdam, North-Holland. | MR | Zbl

[7] J. M. Hyman, B. Nicolaenko, 1986, The Kuramoto-Sivashinsky equation : A bridge betwee PDE'S and dynamical systems, Physica, 18D, pp. 113-126. | MR | Zbl

[8] J. M. Jolly, I. G. Kevrekidis, E. S. Titi, 1990, Approximate inertial manifolds for the Kuramoto-Sivashinsky equation; analysis and computations, Physica, 44D, pp. 38-60. | MR | Zbl

[9] O. Karakashian, G. D. Akrivis, V. A. Dougalis, 1993, On optimal-order error estimates for the nonlinear Schrödinger equation, SIAM J. Numer. Anal., 30, pp. 377-400. | MR | Zbl

[10] O. Karakashian, W. Mckinney, 1990, On optimal high order in time approximations for the Korteweg-de Vries equation, Math. Comp., 55, pp. 473-496. | MR | Zbl

[11] I. G. Kevrekidis, B. Nicolaenko, J. C. Scovel, 1990, Back in the saddle again; a computer assisted study of the Kuramoto-Sivashinsky equation, SIAM J. Appl. Math., 50, pp. 760-790. | MR | Zbl

[12] Y. Kuramoto, 1978, Diffusion induced chaos in reaction Systems, Progr. Theoret. Phys. Suppl., 64, pp. 346-367.

[13] B. Nicolaenko, B. Scheurer, 1984, Remarks on the Kuramoto-Sivashinsky equation, Physica, 12D, pp. 391-395. | MR | Zbl

[14] B. Nicolaenko, B. Scheurer, R. Temam, 1985, Some global dynamical properties of the Kuramoto-Sivashinsky equation : Nonlinear stability and attractors, Physica, 16D, pp. 155-183. | MR | Zbl

[15] J. Nitsche, 1969, Umkehrsätze für Spline-Approximationen, Compositio Mathematica, 21, pp. 400-416. | Numdam | MR | Zbl

[16] J. Nitsche, 1969, Verfahren von Ritz und Spline-Interpolation bei Sturm-Liouville-Randwertproblemen, Numer. Math., 13, pp. 260-265. | MR | Zbl

[17] R. Osserman, 1978, The isoperimetric inequality, Bulletin of the A.M.S., 84, pp. 1182-1238. | MR | Zbl

[18] D. T. Papageorgiou, C. Maldarelli, D. S. Rumschitzki, 1990, Nonlinear interfacial stability of core-annular film flows, Phys. Fluids, A2, pp. 340-352. | MR | Zbl

[19] D. T. Papageorgiou, Y. S. Smyrlis, 1991, The route to chaos for the Kuramoto-Sivashinsky equation, Theoret. Comput. Fluid Dynamics, 3, pp. 15-42. | Zbl

[20] L. L. Schumaker, 1980, Spline Functions : Basic Theory, New York, John Wiley and Sons, Inc. | MR | Zbl

[21] G. Sivashinsky, 1980, On flame propagation under conditions of stoichiometry, SIAM J. Appl. Math, 39, pp. 67-72. | MR | Zbl

[22] E. Tadmor, 1986, The well-posedness of the Kuramoto-Sivashinsky equation, SIAM J. Math. Anal, 17, pp. 884-893. | MR | Zbl

[23] R. Temam, 1988, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, New York : Springer-Verlag. | MR | Zbl

[24] V. Thomée, B. Wendroff, 1974, Convergence estimates for Galerkin methods for variable coefficient initial value problems, SIAM J. Numer. Anal., 11,pp. 1059-1068. | MR | Zbl