A Flexible Galerkin Finite Element Method with an A Posteriori Discontinuous Finite Element Error Estimation for Hyperbolic Problems

A Flexible Galerkin Finite Element Method (FGM) is a hybrid class of finite element methods that combine the usual continuous Galerkin method with the now popular discontinuous Galerkin method (DGM). A detailed description of the formulation of the FGM on a hyperbolic partial differential equation, as well as the data structures used in the FGM algorithm is presented. Some hp-convergence results and computational cost are included. Additionally, an a posteriori error estimate for the DGM applied to a two-dimensional hyperbolic partial differential equation is constructed. Several examples, both linear and nonlinear, indicating the effectiveness of the error estimate are included.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2002

Author dc:creator

• Massey, Thomas Christopher

Chair dc:contributor.committeechair

• Adjerid, Slimane

Committee members dc:contributor.committeemember

• Johnson, Lee W.
• Beattie, Christopher A.
• Borggaard, Jeffrey T.
• Rogers, Robert C.

• a posteriori error estimation
• finite elements
• flexible discontinuous Galerkin
• hyperbolic partial differential equations

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Dc Identifier Other

etd-07102002-142105

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28245