@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}, publisher = {Elsevier}, volume = {32}, number = {6}, year = {1998}, mrnumber = {1652609}, zbl = {0914.65094}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.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. http://archive.numdam.org/item/M2AN_1998__32_6_715_0/
[1] Preserving symmetries in the proper orthogonal decomposition, SIAM J. Sci. Comp., 14, 483-505, 1993. | MR | Zbl
, and ,[2] Some computational aspects on approximate inertial manifolds and finite differences. Discrete and Continuous Dynamical Systems, 2, 417-454, 1996. | MR | Zbl
,[3] 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.
, , , and ,[4] Incremental unknowns for solving partial differential equations. Numerische Mathematik, 59, 255-271, 1991. | MR | Zbl
and .[5] Nonlinear Galerkin method in the finite difference case and wavelet-like incremental-unknowns. Numerische Mathematik, 64(3), 271-294, 1993. | MR | Zbl
and ,[6] Nonlinear Galerkin method with multilevel incremental-unknowns. In E.P. Agarwal, editor, Contributions in Numerical Mathematics, pages 151-164. WSSIAA, 1993. | MR | Zbl
and ,[7] Software for continuation and bifurcation problems in ordinary differential equations. CRPC-95-2, Center for Research on Parallel Computing, California Institute of Technology, 1995.
, and .[8] Dissipativity of numerical schemes. Nonlinearity, pages 591-613, 1991. | MR | Zbl
, , and .[9] Modeling of the interaction of small and large eddies in two dimensional turbulent flows. Math. Model. and Num. Anal., 22(1), 1988. | Numdam | MR | Zbl
, and .[10] Determining nodes, finite difference schemes and inertial manifolds. Nonlinearity, 4, 135-153, 1991. | MR | Zbl
and[11] Matrix Computations. The John Hopkins University Press, second edition, 1989. | MR | Zbl
and .[12] Asymptotic Behavior of Dissipative Systems. AMS, 1988. | MR | Zbl
.[13] Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces. Physica D, 23, 265-292, 1986. | MR | Zbl
, and[14] Explicit construction of an inertial manifold for a reaction diffusion equation. J. Diff. Eq., 78, 220-261, 1989. | MR | Zbl
[15] Approximate inertial manifolds for the Kuramoto-Sivashinsky equation : Analysis and computations. Physica D, 44, 38-60, 1990. | MR | Zbl
, and .[16] Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation. J. Dyn. Diff. Eq., 3, 179-197, 1991. | MR | Zbl
, and .[17] On the effectiveness of the approximate inertial manifold-a computational study, to appear in Theoretical and Computational Fluid Dynamics, 1995. | Zbl
, and .[18] Enslaved finite difference schemes for nonlinear dissipative pdes. Num. Meth. for PDEs, page to appear. | MR | Zbl
, and .[19] Back in the saddle again : A computer assisted study of the Kuramoto-Sivashinsky equation. Siam J. Apl. Math., 50, 760-790, 1990. | MR | Zbl
, and .[20] A finite difference scheme for Computing inertial manifolds. Z angew Math. Phys., 46, 419-444, 1995. | MR | Zbl
and .[21] An approximate inertial manifold for computing Burger's equation. Physica D, 60, 175-184, 1992. | MR | Zbl
and .[22] Approximate inertial manifolds for reaction-diffusion equations in high space dimension. J. Dyn. Diff. Eq., 1, 245-267, 1989. | MR | Zbl
,[23] Nonlinear Galerkin methods. SIAM J. Num. An., 26, 1139-1157, 1989. | MR | Zbl
and .[24] Some global dynamical properties of the Kuramoto-Sivashinsky equation : Nonlinear stability and attractors. Physica D, 16, 155-183, 1985. | MR | Zbl
, and .[25] Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer Verlag, 1988. | MR | Zbl
.[26] Numerical solution of a nonlinear dissipative System using a pseudospectral method and inertial manifolds. Siam J. Sci. Comput., 16, 1049-1070, 1994. | MR | Zbl
and .