High-order accurate, fully discrete entropy stable schemes for scalar conservation laws

Abstract

The recently developed TECNO schemes for hyperbolic conservation laws are designed to be high-order accurate and entropy stable, but are, as of yet, only semidiscrete. We perform an explicit discretization of the temporal derivative to obtain a fully discrete scheme, and derive a rather unrestrictive CFL condition that ensures global entropy stability. The scheme is tested in a series of numerical experiments.