Convergence of a generalized Riemann problem scheme for the Burgers equation

Maria Lukacova-Medvidova; Yuhuan Yuan

Convergence of a generalized Riemann problem scheme for the Burgers equation

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arxiv 2401.03714 v1 pith:V4D4RY7A submitted 2024-01-08 math.NA cs.NA

Maria Lukacova-Medvidova , Yuhuan Yuan This is my paper

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keywords schemeconvergencegeneralizedproblemriemannaddingapproximationartificial

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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.

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