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. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/28245 |
| Date | 15 July 2002 |
| Creators | Massey, Thomas Christopher |
| Contributors | Mathematics, Adjerid, Slimane, Johnson, Lee W., Beattie, Christopher A., Borggaard, Jeffrey T., Rogers, Robert C. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | main.pdf |
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