Methods and Applications of Analysis
Volume 26 (2019)
On the wavewise entropy inequalities for high-resolution schemes with source terms II: the fully-discrete case
Pages: 297 – 318
We extend the framework and the convergence criteria of wavewise entropy inequalitiesof H. Yang  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  on wave trackingand wave analysis and the theory of Vol’pert  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 , were established by the author .
conservation laws with source terms, WEI framework, entropy convergence criteria
2010 Mathematics Subject Classification
Primary 65M12. Secondary 35L60.
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