Massey, Thomas Christopher2014-03-142014-03-142002-07-03etd-07102002-142105http://hdl.handle.net/10919/28245A 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.In Copyrighta posteriori error estimationfinite elementsflexible discontinuous Galerkinhyperbolic partial differential equationsDissertationhttp://scholar.lib.vt.edu/theses/available/etd-07102002-142105/