A Discontinuous Galerkin - Front Tracking Scheme and its Optimal -Optimal Error Estimation
Date of Award
Doctor of Philosophy (Ph.D.)
Tong Sun (Advisor)
Arthur Brecher (Other)
So-Hsiang Chou (Committee Member)
Gordon Wade (Committee Member)
In  and , 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  is generalized to this particular case of a discontinuous solution.
Fode, Adamou M., "A Discontinuous Galerkin - Front Tracking Scheme and its Optimal -Optimal Error Estimation" (2014). Mathematics Ph.D. Dissertations. 68.