A Class of Numerical Algorithms for Large Time Integration: The Nonlinear Galerkin Methods

The nonlinear Galerkin methods are numerical schemes well adapted to the long-term integration of evolution partial differential equations. They consist of looking for approximate solutions lying in nonlinear manifolds that are "close" (in some sense) to the attractor. The aim of this pape...

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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 29; no. 2; pp. 462 - 483
Main Authors: Devulder, Christophe, Marion, Martine
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.04.1992
Subjects:
A priori knowledge
Algorithms
Approximation
Differential equations
Eigenvalues
Eigenvectors
Estimation methods
Exact sciences and technology
Galerkin methods
Hilbert space
Mathematical integration
Mathematical manifolds
Mathematics
Methods
Navier Stokes equation
Navier-Stokes equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical schemes
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Numerical integration
Inertial manifold
Evolution equation
Non linear approximation
Galerkin method
Long term
Partial differential equation
ISSN:0036-1429, 1095-7170
Online Access:Get full text
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Summary:The nonlinear Galerkin methods are numerical schemes well adapted to the long-term integration of evolution partial differential equations. They consist of looking for approximate solutions lying in nonlinear manifolds that are "close" (in some sense) to the attractor. The aim of this paper is to extend these schemes to a large class of manifolds. Convergence results are derived for the schemes introduced.
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ISSN:0036-1429
1095-7170
DOI:10.1137/0729028