Title page for ETD etd-07102002-142105


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
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
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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