Analysis and applications of discontinuous Galerkin methods for hyperbolic equations
Authors
Yang, He
ORCID
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Other Contributors
Li, Fengyan
Schwendeman, Donald W.
McLaughlin, Joyce
Zhang, Lucy T.
Schwendeman, Donald W.
McLaughlin, Joyce
Zhang, Lucy T.
Issue Date
2014-08
Keywords
Mathematics
Degree
PhD
Terms of Use
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
Full Citation
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.
Description
August 2014
School of Science
School of Science
Department
Dept. of Mathematical Sciences
Publisher
Rensselaer Polytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
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