Applications of the nonlinear galerkin methods to some flow problems

2008 ◽  
pp. 230-240
Author(s):  
Kunt Atalık ◽  
Akın Tezel
Keyword(s):  
Galerkin Methods ◽  
Flow Problems ◽  
Nonlinear Galerkin Methods

Nonlinear Galerkin methods for a system of PDEs with Turing instabilities

CALCOLO ◽  
2018 ◽  
Vol 55 (1) ◽  
Author(s):  
Konstantinos Spiliotis ◽  
Lucia Russo ◽  
Francesco Giannino ◽  
Salvatore Cuomo ◽  
Constantinos Siettos ◽  
...  
Keyword(s):  
Galerkin Methods ◽  
Turing Instabilities ◽  
Nonlinear Galerkin Methods

Implementation of finite element nonlinear Galerkin methods using hierarchical bases

1993 ◽  
Vol 11 (5-6) ◽  
pp. 384-407 ◽  
Author(s):  
Jacques Laminie ◽  
Fr�d�ric Pascal ◽  
Roger Temam
Keyword(s):  
Finite Element ◽  
Galerkin Methods ◽  
Hierarchical Bases ◽  
Nonlinear Galerkin Methods

Nonlinear Galerkin Methods

1989 ◽  
Vol 26 (5) ◽  
pp. 1139-1157 ◽  
Author(s):  
Martine Marion ◽  
Roger Temam
Keyword(s):  
Galerkin Methods ◽  
Nonlinear Galerkin Methods

scholarly journals Nonlinear Galerkin Methods for 3D Magnetohydrodynamic Equations

1997 ◽  
Vol 07 (07) ◽  
pp. 1497-1507 ◽  
Author(s):  
Olaf Schmidtmann ◽  
Fred Feudel ◽  
Norbert Seehafer
Keyword(s):  
Partial Differential Equations ◽  
Exact Solutions ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Galerkin Approximation ◽  
Inertial Manifold ◽  
Galerkin Methods ◽  
Magnetohydrodynamic Equations ◽  
Nonlinear Galerkin Method ◽  
Nonlinear Galerkin Methods

The usage of nonlinear Galerkin methods for the numerical solution of partial differential equations is demonstrated by treating an example. We describe the implementation of a nonlinear Galerkin method based on an approximate inertial manifold for the 3D magnetohydrodynamic equations and compare its efficiency with the linear Galerkin approximation. Special bifurcation points, time-averaged values of energy and enstrophy as well as Kaplan–Yorke dimensions are calculated for both schemes in order to estimate the number of modes necessary to correctly describe the behavior of the exact solutions.

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