On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation

DOI10.1016/0375-9601(94)90926-1zbMath0941.65526OpenAlexW1992992086MaRDI QIDQ1964820

Ioannis G. Kevrekidis, Edriss S. Titi, Michael S. Jolly, Ciprian Foias

Publication date: 6 February 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0375-9601(94)90926-1

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) PDEs in connection with fluid mechanics (35Q35) Nonlinear differential equations in abstract spaces (34G20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Cites Work

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• Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
• An approximate inertial manifold for computing Burgers' equation
• On approximate inertial manifolds to the Navier-Stokes equations
• Construction of inertial manifolds by elliptic regularization
• Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension
• Spectral barriers and inertial manifolds for dissipative partial differential equations
• Approximate inertial manifolds for reaction-diffusion equations in high space dimension
• Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
• Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
• Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces
• Inertial manifolds for nonlinear evolutionary equations
• The algebraic approximation of attractors: The finite dimensional case
• Preserving dissipation in approximate inertial forms for the Kuramoto- Sivashinsky equation
• Gevrey class regularity and approximate inertial manifolds for the Kuramoto-Sivashinsky equation
• Infinite-dimensional dynamical systems in mechanics and physics
• Integral manifolds and inertial manifolds for dissipative partial differential equations
• Global analysis of the phase portrait for the Kuramoto-Sivashinsky equation
• Computational efficiency and approximate inertial manifolds for a Bénard convection system
• Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study
• A global attracting set for the Kuramoto-Sivashinsky equation
• The steady states of the Kuramoto-Sivashinsky equation
• Unconditional stability and long-term behavior of transient algorithms for the incompressible Navier-Stokes and Euler equations
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
• Determining nodes, finite difference schemes and inertial manifolds
• Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation
• Approximate inertial manifolds and effective viscosity in turbulent flows
• Dissipativity of numerical schemes
• Modelling of the interaction of small and large eddies in two dimensional turbulent flows
• Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation
• Regularity of solutions and the convergence of the galerkin method in the ginzburg-landau equation
• A Remark on Quasi-Stationary Approximate Inertial Manifolds for the Navier–Stokes Equations
• Nonlinear Galerkin Methods
• Long time stability and convergence for fully discrete nonlinear galerkin methods
• Some Numerical Aspects of Computing Inertial Manifolds
• On the Rate of Convergence of the Nonlinear Galerkin Methods