Convergence of MUSCL relaxing schemes to the relaxed schemes for conservation laws with stiff source terms

Tao TANG; J. Wang

doi:10.1023/A:1007681726414

Convergence of MUSCL relaxing schemes to the relaxed schemes for conservation laws with stiff source terms

Tao TANG^*, J. Wang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We consider the convergence and stability property of MUSCL relaxing schemes applied to conservation laws with stiff source terms. The maximum principle for the numerical schemes will be established. It will be also shown that the MUSCL relaxing schemes are uniformly l¹- and TV-stable in the sense that they are bounded by a constant independent of the relaxation parameter ε, the Lipschitz constant of the stiff source term and the time step Δt. The Lipschitz constant of the l¹ continuity in time for the MUSCL relaxing schemes is shown to be independent of ε and Δt. The convergence of the relaxing schemes to the corresponding MUSCL relaxed schemes is then established.

Original language	English
Pages (from-to)	173-195
Number of pages	23
Journal	Journal of Scientific Computing
Volume	15
Issue number	2
DOIs	https://doi.org/10.1023/A:1007681726414
Publication status	Published - Jun 2000

Scopus Subject Areas

Software
Theoretical Computer Science
Numerical Analysis
Engineering(all)
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Convergence
Maximum principle
Nonlinear conservation laws
Relaxation scheme

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10.1023/A:1007681726414

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title = "Convergence of MUSCL relaxing schemes to the relaxed schemes for conservation laws with stiff source terms",

abstract = "We consider the convergence and stability property of MUSCL relaxing schemes applied to conservation laws with stiff source terms. The maximum principle for the numerical schemes will be established. It will be also shown that the MUSCL relaxing schemes are uniformly l1- and TV-stable in the sense that they are bounded by a constant independent of the relaxation parameter ε, the Lipschitz constant of the stiff source term and the time step Δt. The Lipschitz constant of the l1 continuity in time for the MUSCL relaxing schemes is shown to be independent of ε and Δt. The convergence of the relaxing schemes to the corresponding MUSCL relaxed schemes is then established.",

keywords = "Convergence, Maximum principle, Nonlinear conservation laws, Relaxation scheme",

author = "Tao TANG and J. Wang",

note = "Funding Information: We thank the referee for the comments on the accuracy of the relaxed scheme. This research was supported in part by Hong Kong Baptist University and Hong Kong Research Grants Council. The research of the second author was also supported by the National Natural Science Foundation of China and U.S.-China Joint Research Proposal INT-9601376.",

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T1 - Convergence of MUSCL relaxing schemes to the relaxed schemes for conservation laws with stiff source terms

AU - TANG, Tao

AU - Wang, J.

N1 - Funding Information: We thank the referee for the comments on the accuracy of the relaxed scheme. This research was supported in part by Hong Kong Baptist University and Hong Kong Research Grants Council. The research of the second author was also supported by the National Natural Science Foundation of China and U.S.-China Joint Research Proposal INT-9601376.

PY - 2000/6

Y1 - 2000/6

N2 - We consider the convergence and stability property of MUSCL relaxing schemes applied to conservation laws with stiff source terms. The maximum principle for the numerical schemes will be established. It will be also shown that the MUSCL relaxing schemes are uniformly l1- and TV-stable in the sense that they are bounded by a constant independent of the relaxation parameter ε, the Lipschitz constant of the stiff source term and the time step Δt. The Lipschitz constant of the l1 continuity in time for the MUSCL relaxing schemes is shown to be independent of ε and Δt. The convergence of the relaxing schemes to the corresponding MUSCL relaxed schemes is then established.

AB - We consider the convergence and stability property of MUSCL relaxing schemes applied to conservation laws with stiff source terms. The maximum principle for the numerical schemes will be established. It will be also shown that the MUSCL relaxing schemes are uniformly l1- and TV-stable in the sense that they are bounded by a constant independent of the relaxation parameter ε, the Lipschitz constant of the stiff source term and the time step Δt. The Lipschitz constant of the l1 continuity in time for the MUSCL relaxing schemes is shown to be independent of ε and Δt. The convergence of the relaxing schemes to the corresponding MUSCL relaxed schemes is then established.

KW - Convergence

KW - Maximum principle

KW - Nonlinear conservation laws

KW - Relaxation scheme

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DO - 10.1023/A:1007681726414

M3 - Article

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JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 2

ER -

Convergence of MUSCL relaxing schemes to the relaxed schemes for conservation laws with stiff source terms

Abstract

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