On the Rate of Convergence of the Nonlinear Galerkin Methods

DOI10.2307/2153099zbMath0783.65053OpenAlexW4238937692MaRDI QIDQ5288217

Edriss S. Titi, Christophe Devulder, Martine Marion

Publication date: 15 August 1993

Full work available at URL: https://doi.org/10.2307/2153099

zbMATH Keywords

rate of convergencenonlinear Galerkin method

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Nonlinear differential equations in abstract spaces (34G20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (27)

A finite difference scheme for computing inertial manifolds ⋮ On the effectiveness of the approximate inertial manifold -- a computational study ⋮ On computing the long-time solution of the two-dimensional Navier-Stokes equations ⋮ Some closure results for inertial manifolds ⋮ A two-level method in time and space for solving the Navier-Stokes equations based on Newton iteration ⋮ A new nonlinear Galerkin finite element method for the computation of reaction diffusion equations ⋮ Uniform-in-Time Error Estimates for the Postprocessing Galerkin Method Applied to a Data Assimilation Algorithm ⋮ Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations ⋮ A posteriori regularity of the three-dimensional Navier–Stokes equations from numerical computations ⋮ On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation ⋮ Stability and convergence of optimum spectral non-linear Galerkin methods ⋮ Taylor expansion method for nonlinear evolution equations ⋮ Hausdorff dimension of functionally invariant sets for rotating internal weakly viscoelastic fluids ⋮ Determining finite volume elements for the 2D Navier-Stokes equations ⋮ An approximate inertial manifold for computing Burgers' equation ⋮ A modified nonlinear Galerkin method for the viscoelastic fluid motion equations ⋮ Stability and convergence of the reform postprocessing Galerkin method ⋮ Multi-level spectral Galerkin method for the Navier-Stokes equations. II: Time discretization ⋮ Fourier collocation splittings for partial differential equations ⋮ Variational approach to closure of nonlinear dynamical systems: autonomous case ⋮ A two-level method in space and time for the Navier-Stokes equations ⋮ Multi-level spectral Galerkin method for the Navier-Stokes problem. I: Spatial discretization ⋮ Postprocessing Fourier spectral methods: The case of smooth solutions ⋮ Numerical analysis of the Navier-Stokes equations ⋮ An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations ⋮ Convergence of a chaotic attractor with increased spatial resolution of the Ginzburg-Landau equation. ⋮ Computational efficiency and approximate inertial manifolds for a Bénard convection system

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