Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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: 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.


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


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