Mathematics Ph.D. Dissertations
Error analysis of the cubic front tracking and RKDG method for one dimensional conservation laws
Date of Award
2018
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.)
Department
Mathematics
First Advisor
Tong Sun (Advisor)
Second Advisor
Andrew Layden (Committee Member)
Third Advisor
Juan Bes (Committee Member)
Fourth Advisor
So-Hsiang Chou (Committee Member)
Abstract
The error analysis for the Runge-Kutta discontinuous Galerkin (RKDG) method for solving the scalar nonlinear conservation laws for the case of a smooth solution has been given in [23] and for the case of having a fully developed shock has given in [22]. We use the Cubic Front Tracking and RKDG method to obtain the solution for the case between [23] and [22] where a shock is forming but not fully developed yet. The numerical smoothness approach used in [23] is generalized for the case between [23] and [22].
Recommended Citation
Bhusal, Raju Prasad, "Error analysis of the cubic front tracking and RKDG method for one dimensional conservation laws" (2018). Mathematics Ph.D. Dissertations. 16.
https://scholarworks.bgsu.edu/math_diss/16