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Error Analysis of RKDG Methods for 1-D Hyperbolic Conservation Laws

Rumsey, David
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1332186614

Abstract Details

2012, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics and Statistics.
Obtaining reasonable error estimates for computed solutions to hyperbolic conservation laws using the Runge-Kutta / Discontinuous Galerkin Method (RKDG) has been an issue for many years. Zhang and Shu have written papers dealing with an a priori estimate for a third order Runge-Kutta scheme. In this dissertation a new way to compute an a posteriori error estimate for numerical solutions computed using RKDG methods is provided. These techniques can be applied to any order Runge-Kutta scheme as well as any order polynomial. The idea of smoothness indicators is discussed in the papers by Sun, Sun and Fillippova, and Rumsey and Sun. These smoothness indicators are used to compute an a posteriori error estimate. In providing the framework for this new technique, only the regions where the solution is smooth are considered. Two examples, Burgers' equation and the traffic law, are provided to give the full details of the error analysis and to show that the errors computed are reasonable. In the final remarks some insight into how to adapt this method for regions where the solution has a fully developed shock or a partially developed shock are discussed.
Tong Sun, PhD (Committee Chair)
Kit Chan, PhD (Committee Member)
So-Hsiang Chou, PhD (Committee Member)
John Laird, PhD (Committee Member)
Applied Mathematics; Mathematics
RKDG; conservation law; error analysis; hyperbolic

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Citations

  • Rumsey, D. (2012). Error Analysis of RKDG Methods for 1-D Hyperbolic Conservation Laws [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1332186614

    APA Style (7th edition)

  • Rumsey, David. Error Analysis of RKDG Methods for 1-D Hyperbolic Conservation Laws. 2012. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1332186614.

    MLA Style (8th edition)

  • Rumsey, David. "Error Analysis of RKDG Methods for 1-D Hyperbolic Conservation Laws." Doctoral dissertation, Bowling Green State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1332186614

    Chicago Manual of Style (17th edition)

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© 2012, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.