Type of Document	Dissertation
Author	Massey, Thomas Christopher
Author's Email Address	thmassey@math.vt.edu
URN	etd-07102002-142105
Title	A Flexible Galerkin Finite Element Method with an A Posteriori Discontinuous Finite Element Error Estimation for Hyperbolic Problems
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title Slimane Adjerid Committee Chair Christopher Beattie Committee Member Jeffrey T. Borggaard Committee Member Lee Johnson Committee Member Robert C. Rogers Committee Member
Keywords	a posteriori error estimation finite elements flexible discontinuous Galerkin hyperbolic partial differential equations
Date of Defense	2002-07-03
Availability	unrestricted
Abstract 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.
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