Inertial Manifolds and Nonlinear Galerkin Methods

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2005

Author dc:creator

• Kovacs, Denis Christoph

Chairs dc:contributor.committeechair

• Borggaard, Jeffrey T.
• Beattie, Christopher A.

Committee members dc:contributor.committeemember

• Gugercin, Serkan
• Iliescu, Traian

• inertial manifolds
• nonlinear Galerkin
• postprocessed Galerkin
• approximate inertial manifolds

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-01032006-110416

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/30792