A Discontinuous Galerkin - Front Tracking Scheme and its Optimal² Error Estimation

2013/12/09 by Sun, Tong, Fode, Adamou
#65N12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1312.2519

Abstract

In [11] and [5], 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 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.

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