Analysis and applications of discontinuous Galerkin methods for hyperbolic equations

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Authors
Yang, He
Issue Date
2014-08
Type
Electronic thesis
Thesis
Language
ENG
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Mathematics
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Abstract
Dispersion and dissipation errors are especially important for long time wave simulations. In the first part of the thesis, we study the dispersion and dissipation errors of two fully discrete DG methods, i.e. Runge-Kutta discontinuous Galerkin (RKDG) and Lax-Wendroff discontinuous Galerkin (LWDG) methods. After deriving the analytical formulations of the dispersion and dissipation errors as functions of the CFL number, we further investigate the role of spatial DG and temporal discretizations. One important conclusion we draw is that the DG discretizations in space lead to super-convergence in the dispersion analysis. However, such phenomena disappears when DG methods are combined with finite difference types of time integration with a standard CFL number. We then give the CFL conditions under which the super-convergence can be recovered.
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August 2014
School of Science
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Rensselaer Polytechnic Institute, Troy, NY
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