Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On numerical entropy inequalities for a class of relaxed schemes

Authors: Huazhong Tang, Tao Tang and Jinghua Wang
Journal: Quart. Appl. Math. 59 (2001), 391-399
MSC: Primary 65M06; Secondary 35B25, 35L65
DOI: https://doi.org/10.1090/qam/1828460
MathSciNet review: MR1828460
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In [4], Jin and Xin developed a class of first- and second-order relaxing schemes for nonlinear conservation laws. They also obtained the relaxed schemes for conservation laws by using a Hilbert expansion for the relaxing schemes. The relaxed schemes were proved to be total variational diminishing (TVD) in the zero relaxation limit for scalar equations. In this paper, by properly choosing the numerical entropy flux, we show that the relaxed schemes also satisfy the entropy inequalities. As a consequence, the $ {L^{1}}$ convergence rate of $ O\left( \sqrt {\Delta t} \right)$ for the relaxed schemes can be established.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 65M06, 35B25, 35L65

Retrieve articles in all journals with MSC: 65M06, 35B25, 35L65

Additional Information

DOI: https://doi.org/10.1090/qam/1828460
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society