Warburton, Tim2018-12-032018-12-032006Binford, Tommy L., Jr.. "A survey of discontinuous Galerkin methods for solving the time domain Maxwell's equations." (2006) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/103704">https://hdl.handle.net/1911/103704</a>.https://hdl.handle.net/1911/103704The discontinuous Galerkin (DG) method with different numerical fluxes is applied to the square wave guide problem to avoid spurious modes that arise from the application of standard finite element methods. These numerical fluxes are the central, upwind and Lax-Friedrichs found in the literature. A new scheme, called penalty DG, is presented. Each scheme is tested with and without a locally divergence-free basis for the magnetic field. The spectral properties of the DG spatial discretization matrix for each flux are surmised by considering three different meshes and example eigenvalue plots. The convergence rate of the first ten eigenvalues is observed for h - and p -refinements. The central flux scheme is determined to be a poor choice for problems involving Maxwell's equations. It is proved that the kernel is empty for the DG spatial discretization matrix corresponding to the Lax-Friedrichs divergence-free scheme.87 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MathematicsPure sciencesThesis305274055THESIS MATH.SCI. 2007 BINFORD