Type of Document Dissertation Author Massey, Thomas Christopher Author's Email Address firstname.lastname@example.org 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 Adjerid, Slimane Committee Chair Beattie, Christopher A. Committee Member Borggaard, Jeffrey T. Committee Member Johnson, Lee W. Committee Member Rogers, Robert C. Committee Member Keywords
- a posteriori error estimation
- finite elements
- flexible discontinuous Galerkin
- hyperbolic partial differential equations
Date of Defense 2002-07-03 Availability unrestricted AbstractA 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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