On numerical entropy inequalities for a class of relaxed schemes

H. Tang; Tao Tang; J. Wang

doi:10.1090/qam/1828460

On numerical entropy inequalities for a class of relaxed schemes

H. Tang^*, Tao Tang, J. Wang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

2 Citations (Scopus)

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 L¹ convergence rate of O (√Δt) for the relaxed schemes can be established.

Original language	English
Pages (from-to)	391-399
Number of pages	9
Journal	Quarterly of Applied Mathematics
Volume	59
Issue number	2
DOIs	https://doi.org/10.1090/qam/1828460
Publication status	Published - Jun 2001

Scopus Subject Areas

Applied Mathematics

User-Defined Keywords

Hyperbolic conservation laws
Numerical entropy inequality
Relaxed schemes
Relaxing schemes

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10.1090/qam/1828460

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title = "On numerical entropy inequalities for a class of relaxed schemes",

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 L1 convergence rate of O (√Δt) for the relaxed schemes can be established.",

keywords = "Hyperbolic conservation laws, Numerical entropy inequality, Relaxed schemes, Relaxing schemes",

author = "H. Tang and Tao Tang and J. Wang",

note = "The research of the first author was supported by the National Natural Science Foundation of China and the foundation of National key Laboratory of Computational Physics. The research of the second author was supported by Hong Kong Baptist University. The research of the third author was supported in part by the National Natural Science Foundation of China, and in part by NSF of US and NSF of China Joint Research Proposal No. INT-9601376. ",

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doi = "10.1090/qam/1828460",

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T1 - On numerical entropy inequalities for a class of relaxed schemes

AU - Tang, H.

AU - Tang, Tao

AU - Wang, J.

N1 - The research of the first author was supported by the National Natural Science Foundation of China and the foundation of National key Laboratory of Computational Physics. The research of the second author was supported by Hong Kong Baptist University. The research of the third author was supported in part by the National Natural Science Foundation of China, and in part by NSF of US and NSF of China Joint Research Proposal No. INT-9601376.

PY - 2001/6

Y1 - 2001/6

N2 - 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 L1 convergence rate of O (√Δt) for the relaxed schemes can be established.

AB - 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 L1 convergence rate of O (√Δt) for the relaxed schemes can be established.

KW - Hyperbolic conservation laws

KW - Numerical entropy inequality

KW - Relaxed schemes

KW - Relaxing schemes

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DO - 10.1090/qam/1828460

M3 - Journal article

AN - SCOPUS:0035367391

SN - 0033-569X

VL - 59

SP - 391

EP - 399

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

IS - 2

ER -

On numerical entropy inequalities for a class of relaxed schemes

Abstract

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