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].

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