Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations

Bonito, Andrea; Guermond, Jean-Luc; Popov, Bojan

doi:10.1090/S0025-5718-2013-02771-8

Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations
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by Andrea Bonito, Jean-Luc Guermond and Bojan Popov;

Math. Comp. 83 (2014), 1039-1062

DOI: https://doi.org/10.1090/S0025-5718-2013-02771-8

Published electronically: October 3, 2013

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Abstract:

We establish the $L^2$-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First- and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition.

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