Convergence of a generalized Riemann problem scheme for the Burgers equation
Numerical Analysis
2024-01-09 v1 Numerical Analysis
Abstract
In this paper we study the convergence of a second order finite volume approximation of the scalar conservation law. This scheme is based on the generalized Riemann problem (GRP) solver. We firstly investigate the stability of the GRP scheme and find that it might be entropy unstable when the shock wave is generated. By adding an artificial viscosity we propose a new stabilized GRP scheme. Under the assumption that numerical solutions are uniformly bounded, we prove consistency and convergence of this new GRP method.
Keywords
Cite
@article{arxiv.2401.03714,
title = {Convergence of a generalized Riemann problem scheme for the Burgers equation},
author = {Maria Lukacova-Medvidova and Yuhuan Yuan},
journal= {arXiv preprint arXiv:2401.03714},
year = {2024}
}
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24 pages