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A discontinuous Galerkin-front tracking scheme and its optimal-optimal error estimation. (English) Zbl 1330.65154

Summary: An error estimate of optimal convergence rates and optimal error propagation (optimal-optimal) was given for the numerical solutions produced by the Runge-Kutta discontinuous Galerkin (RKDG) method on the scalar nonlinear conservation laws in the case of smooth solutions in [the first author and D. Rumsey, J. Comput. Appl. Math. 241, 68–83 (2013; Zbl 1261.65095)]. 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 [loc. cit.] is generalized to this particular case of a discontinuous solution.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Citations:

Zbl 1261.65095
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References:

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