Title page for ETD etd-01032006-110416


Type of Document Master's Thesis
Author Kovacs, Denis Christoph
Author's Email Address kovacs@vt.edu
URN etd-01032006-110416
Title Inertial Manifolds and Nonlinear Galerkin Methods
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Borggaard, Jeffrey T. Committee Chair
Beattie, Christopher A. Committee Co-Chair
Gugercin, Serkan Committee Member
Iliescu, Traian Committee Member
Keywords
  • inertial manifolds
  • nonlinear Galerkin
  • postprocessed Galerkin
  • approximate inertial manifolds
Date of Defense 2005-12-09
Availability unrestricted
Abstract
Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term is used, a simple postprocessing step yields the same improvements that can be observed with nonlinear Galerkin. We show that this improvement is mainly due to the information about the forcing term that is neglected by standard Galerkin. Moreover, we construct a simple postprocessing scheme that uses only this neglected information but gives the same increase in accuracy as nonlinear or postprocessed Galerkin methods.
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