On the stability and accuracy of high-order Runge-Kutta discontinuous Galerkin methods
Authors
Reyna, Matthew Aaron
ORCID
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Other Contributors
Li, Fengyan
Kovacic, Gregor
Oberai, Assad
Schwendeman, Donald W.
Kovacic, Gregor
Oberai, Assad
Schwendeman, Donald W.
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
Scientific, mathematical, and computational advances have made high-order numerical methods for hyperbolic conservation laws both increasingly important and increasingly accessible. However, various issues with the stability and accuracy of high-order methods can limit the appeal of these schemes. In this thesis, we consider such issues in the context of Runge-Kutta discontinuous Galerkin (RKDG) methods, which combine discontinuous Galerkin (DG) spatial discretizations with Runge-Kutta (RK) temporal discretizations. RKDG methods possess a number of appealing features for the numerical solution of hyperbolic problems, including compactness, adaptivity, high parallelizability, and high-order accuracy.
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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