Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations

  • The usage of nonlinear Galerkin methods for the numerical solution of partial differential equations is demonstrated by treating an example. We desribe 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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Author:Olaf Schmidtmann, Fred Feudel, Norbert Seehafer
Series (Serial Number):NLD Preprints (paper 035)
Document Type:Preprint
Date of Publication (online):2007/06/22
Year of Completion:1997
Publishing Institution:Universität Potsdam
Release Date:2007/06/22
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Wissenschaftliche Einrichtungen / Interdisziplinäres Zentrum Dynamik komplexer Systeme
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik