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

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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 convergence rate of for the relaxed schemes can be established.

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DOI:
https://doi.org/10.1090/qam/1828460

Article copyright:
© Copyright 2001
American Mathematical Society