@article{M2AN_1998__32_6_715_0,
author = {Bronstering, Rolf and Chen, Min},
title = {Bifurcations of finite difference schemes and their approximate inertial forms},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {715--728},
year = {1998},
publisher = {Elsevier},
volume = {32},
number = {6},
mrnumber = {1652609},
zbl = {0914.65094},
language = {en},
url = {https://www.numdam.org/item/M2AN_1998__32_6_715_0/}
}
TY - JOUR AU - Bronstering, Rolf AU - Chen, Min TI - Bifurcations of finite difference schemes and their approximate inertial forms JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1998 SP - 715 EP - 728 VL - 32 IS - 6 PB - Elsevier UR - https://www.numdam.org/item/M2AN_1998__32_6_715_0/ LA - en ID - M2AN_1998__32_6_715_0 ER -
%0 Journal Article %A Bronstering, Rolf %A Chen, Min %T Bifurcations of finite difference schemes and their approximate inertial forms %J ESAIM: Modélisation mathématique et analyse numérique %D 1998 %P 715-728 %V 32 %N 6 %I Elsevier %U https://www.numdam.org/item/M2AN_1998__32_6_715_0/ %G en %F M2AN_1998__32_6_715_0
Bronstering, Rolf; Chen, Min. Bifurcations of finite difference schemes and their approximate inertial forms. ESAIM: Modélisation mathématique et analyse numérique, Tome 32 (1998) no. 6, pp. 715-728. https://www.numdam.org/item/M2AN_1998__32_6_715_0/
[1] , and , Preserving symmetries in the proper orthogonal decomposition, SIAM J. Sci. Comp., 14, 483-505, 1993. | Zbl | MR
[2] , Some computational aspects on approximate inertial manifolds and finite differences. Discrete and Continuous Dynamical Systems, 2, 417-454, 1996. | Zbl | MR
[3] , , , and , The incremental unknowns-multilevel scheme for the simulation of turbulent channel flows. Proceedings of 1996 Summer Program, Center for Turbulence Research, NASA Ames/Stanford Univ., pages 291-308, 1996.
[4] and . Incremental unknowns for solving partial differential equations. Numerische Mathematik, 59, 255-271, 1991. | Zbl | MR
[5] and , Nonlinear Galerkin method in the finite difference case and wavelet-like incremental-unknowns. Numerische Mathematik, 64(3), 271-294, 1993. | Zbl | MR
[6] and , Nonlinear Galerkin method with multilevel incremental-unknowns. In E.P. Agarwal, editor, Contributions in Numerical Mathematics, pages 151-164. WSSIAA, 1993. | Zbl | MR
[7] , and . Software for continuation and bifurcation problems in ordinary differential equations. CRPC-95-2, Center for Research on Parallel Computing, California Institute of Technology, 1995.
[8] , , and . Dissipativity of numerical schemes. Nonlinearity, pages 591-613, 1991. | Zbl | MR
[9] , and . Modeling of the interaction of small and large eddies in two dimensional turbulent flows. Math. Model. and Num. Anal., 22(1), 1988. | Zbl | MR | Numdam
[10] and Determining nodes, finite difference schemes and inertial manifolds. Nonlinearity, 4, 135-153, 1991. | Zbl | MR
[11] and . Matrix Computations. The John Hopkins University Press, second edition, 1989. | Zbl | MR
[12] . Asymptotic Behavior of Dissipative Systems. AMS, 1988. | Zbl | MR
[13] , and Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces. Physica D, 23, 265-292, 1986. | Zbl | MR
[14] Explicit construction of an inertial manifold for a reaction diffusion equation. J. Diff. Eq., 78, 220-261, 1989. | Zbl | MR
[15] , and . Approximate inertial manifolds for the Kuramoto-Sivashinsky equation : Analysis and computations. Physica D, 44, 38-60, 1990. | Zbl | MR
[16] , and . Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation. J. Dyn. Diff. Eq., 3, 179-197, 1991. | Zbl | MR
[17] , and . On the effectiveness of the approximate inertial manifold-a computational study, to appear in Theoretical and Computational Fluid Dynamics, 1995. | Zbl
[18] , and . Enslaved finite difference schemes for nonlinear dissipative pdes. Num. Meth. for PDEs, page to appear. | Zbl | MR
[19] , and . Back in the saddle again : A computer assisted study of the Kuramoto-Sivashinsky equation. Siam J. Apl. Math., 50, 760-790, 1990. | Zbl | MR
[20] and . A finite difference scheme for Computing inertial manifolds. Z angew Math. Phys., 46, 419-444, 1995. | Zbl | MR
[21] and . An approximate inertial manifold for computing Burger's equation. Physica D, 60, 175-184, 1992. | Zbl | MR
[22] , Approximate inertial manifolds for reaction-diffusion equations in high space dimension. J. Dyn. Diff. Eq., 1, 245-267, 1989. | Zbl | MR
[23] and . Nonlinear Galerkin methods. SIAM J. Num. An., 26, 1139-1157, 1989. | Zbl | MR
[24] , and . Some global dynamical properties of the Kuramoto-Sivashinsky equation : Nonlinear stability and attractors. Physica D, 16, 155-183, 1985. | Zbl | MR
[25] . Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer Verlag, 1988. | Zbl | MR
[26] and . Numerical solution of a nonlinear dissipative System using a pseudospectral method and inertial manifolds. Siam J. Sci. Comput., 16, 1049-1070, 1994. | Zbl | MR





