An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations
From MaRDI portal
Publication:4240571
DOI10.1090/S0025-5718-99-01057-1zbMath0930.76063OpenAlexW2091680275MaRDI QIDQ4240571
Bosco García-Archilla, Edriss S. Titi, Julia Novo
Publication date: 28 April 1999
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01057-1
reaction-diffusion systemshomogeneous Dirichlet boundary conditionsspectral methodsCahn-Hilliard equationsdissipative equationsdefect-correction technique
Related Items
Tangent space correction method for the Galerkin approximation based on two-grid finite element, Postprocessing mixed finite element methods for solving Cahn-Hilliard equation: methods and error analysis, A postprocessing mixed finite element method for the Navier–Stokes equations, Adaptive local postprocessing finite element method for the Navier-Stokes equations, Inertial manifold and state estimation of dissipative nonlinear PDE systems, On three steps two-grid finite element methods for the 2D-transient Navier-Stokes equations, Static two-grid mixed finite-element approximations to the Navier-Stokes equations, Superconvergence of the effective Cauchy stress in computational homogenization of inelastic materials, A new error analysis and post-processing technique of the lowest-order Raviart-Thomas mixed finite element method for parabolic problems, Reduced and bifurcation analysis of intrinsically bursting neuron model, Uniform-in-Time Error Estimates for the Postprocessing Galerkin Method Applied to a Data Assimilation Algorithm, Two-grid mixed finite-element approximations to the Navier-Stokes equations based on a Newton-type step, Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations, Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equations, A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations, An enhanced pseudospectral Chebyshev method for dissipative partial differential equations, Taylor expansion method for nonlinear evolution equations, A two-grid finite difference method for the primitive equations of the ocean, Superconvergence of elliptic reconstructions of finite element solutions of parabolic problems in domains with piecewise smooth boundaries, Galerkin and subspace decomposition methods in space and time for the Navier-Stokes equations, A two-level finite element method for the Navier-Stokes equations based on a new projection, Stability and convergence of the reform postprocessing Galerkin method, Holistic discretization ensures fidelity to Burgers' equation, REGULARITY CONSTANTS OF THE STOKES PROBLEM: APPLICATION TO FINITE-ELEMENT METHODS ON CURVED DOMAINS, An AIM and one-step Newton method for the Navier-Stokes equations, A novel order reduction method for nonlinear dynamical system under external periodic excitations, A two-level correction method in space and time based on Crank–Nicolson scheme for Navier–Stokes equations, Multi-level spectral Galerkin method for the Navier-Stokes equations. II: Time discretization, A subgrid stabilizing postprocessed mixed finite element method for the time-dependent Navier-Stokes equations, An Oseen-Type Post-Processed Finite Element Method Based on a Subgrid Model for the Time-Dependent Navier–Stokes Equations, Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations, A posteriori error estimates for fully discrete nonlinear parabolic problems, 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, A modified nonlinear spectral Galerkin method for the equations of motion arising in the Kelvin–Voigt fluids
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
- A nonlinear Galerkin method for the Navier-Stokes equations
- On approximate inertial manifolds to the Navier-Stokes equations
- Nonlinear Galerkin methods: The finite elements case
- Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
- Inertial manifolds for nonlinear evolutionary equations
- The algebraic approximation of attractors: The finite dimensional case
- Geometric theory of semilinear parabolic equations
- Preserving dissipation in approximate inertial forms for the Kuramoto- Sivashinsky equation
- Infinite-dimensional dynamical systems in mechanics and physics
- On the construction of families of approximate inertial manifolds
- Nonlinear Galerkin methods and mixed finite elements: Two-grid algorithms for the Navier-Stokes equations
- Generalized Stokes eigenfunctions: A new trial basis for the solution of incompressible Navier-Stokes equations
- Subgrid modelling and the interaction of small and large wavelength in turbulent flows
- On the effectiveness of the approximate inertial manifold -- a computational study
- \(C^ 1\) approximations of inertial manifolds for dissipative nonlinear equations
- Modelling of the interaction of small and large eddies in two dimensional turbulent flows
- Nonlinear Schrödinger evolution equations
- On the Solution of Nonlinear Finite Element Systems
- Analysis of a Multilevel Iterative Method for Nonlinear Finite Element Equations
- A Class of Numerical Algorithms for Large Time Integration: The Nonlinear Galerkin Methods
- A Galerkin Method for a Nonlinear Dirichlet Problem
- A Novel Two-Grid Method for Semilinear Elliptic Equations
- Singularities Produced in Conormal Wave Interactions
- Postprocessing the Galerkin Method: a Novel Approach to Approximate Inertial Manifolds
- Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
- Nonlinear Galerkin Methods
- Long time stability and convergence for fully discrete nonlinear galerkin methods
- Time integration of the non-linear Galerkin method
- Numerical Solution of a Nonlinear Dissipative System Using a Pseudospectral Method and Inertial Manifolds
- Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements
- Postprocessing the Galerkin Method: The Finite-Element Case
- On the Rate of Convergence of the Nonlinear Galerkin Methods