On the wavewise entropy inequalities for high-resolution schemes with source terms II: the fully-discrete case

We extend the framework and the convergence criteria of wavewise entropy inequalitiesof H. Yang [35] to a class of fully-discrete high-resolution schemes for hyperbolic conservationlaws with source terms. This approach is based on an extended theory of Yang [35] on wave trackingand wave analysis and the theory of Vol’pert [33] on BV solutions. For the Cauchy problem of convexconservation laws with source terms, we use one of the criteria to show the entropy convergence ofthe schemes with van Leer’s flux limiter when the building block of the schemes is the Godunovor Engquish–Osher. The entropy convergence of the homogeneous counterparts of these schemes,originally introduced by Sweby [30], were established by the author [17].

Keywords

conservation laws with source terms, WEI framework, entropy convergence criteria

2010 Mathematics Subject Classification

Primary 65M12. Secondary 35L60.

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This paper is dedicated to Professor Huanan Yang in memory of his extraordinary contribution for establishing WEI framework.

Received 17 November 2016

Accepted 22 March 2019

Published 13 May 2020