Mathematics Ph.D. Dissertations


A Discontinuous Galerkin - Front Tracking Scheme and its Optimal -Optimal Error Estimation

Date of Award


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)


Mathematics/Mathematics (Pure)

First Advisor

Tong Sun (Advisor)

Second Advisor

Arthur Brecher (Other)

Third Advisor

So-Hsiang Chou (Committee Member)

Fourth Advisor

Gordon Wade (Committee Member)


In [28] and [13], an error estimate of optimal convergence rates and optimal error propagation (optimal2) was given for the Runge-Kutta discontinuous Galerkin (RKDG) method solving the scalar nonlinear conservation laws in the case of smooth solutions. This dissertation generalizes the problem to the case of a piecewise smooth solution containing one fully developed shock. A front tracking technique is incorporated in the RKDG scheme to produce a numerical solution with a truly high order error. The numerical smoothness approach of [28] is generalized to this particular case of a discontinuous solution.