A Discontinuous Galerkin - Front Tracking Scheme and its Optimal$^2$ Error Estimation
Numerical Analysis
2013-12-10 v1
Abstract
In [11] and [5], an error estimate of optimal convergence rates and optimal error propagation (optimal^2) was given for the Runge-Kutta discontinuous Galerkin (RKDG) method solving the scalar nonlinear conservation laws in the case of smooth solutions. This manuscript 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 [11] is generalized to this particular case of a discontinuous solution.
Cite
@article{arxiv.1312.2519,
title = {A Discontinuous Galerkin - Front Tracking Scheme and its Optimal$^2$ Error Estimation},
author = {Tong Sun and Adamou Fode},
journal= {arXiv preprint arXiv:1312.2519},
year = {2013}
}
Comments
21 pages, 8 figures from jpeg file, 2 more pictures plotted by latex, 6 tables produced by latex