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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Metadaten
Author details:Olaf Schmidtmann, Fred Feudel, Norbert SeehaferORCiD
URN:urn:nbn:de:kobv:517-opus-14431
Publication series (Volume number):NLD Preprints (35)
Publication type:Preprint
Language:English
Publication year:1997
Publishing institution:Universität Potsdam
Release date:2007/06/22
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Zentrale und wissenschaftliche Einrichtungen / Interdisziplinäres Zentrum für Dynamik komplexer Systeme
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
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