Maximum principle and convergence of central schemes based on slope limiters

Orhan Mehmetoglu; Bojan Popov

doi:10.1090/s0025-5718-2011-02514-7

Maximum principle and convergence of central schemes based on slope limiters

Orhan Mehmetoglu, Bojan Popov

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

4 Scopus citations

Abstract

A maximum principle and convergence of second order central schemes is proven for scalar conservation laws in dimension one. It is well known that to establish a maximum principle a nonlinear piecewise linear reconstruction is needed and a typical choice is the minmod limiter. Unfortunately, this implies that the scheme uses a first order reconstruction at local extrema. The novelty here is that we allow local nonlinear reconstructions which do not reduce to first order at local extrema and still prove maximum principle and convergence. © 2011 American Mathematical Society.

Original language	English (US)
Pages (from-to)	219-231
Number of pages	13
Journal	Mathematics of Computation
Volume	81
Issue number	277
DOIs	https://doi.org/10.1090/s0025-5718-2011-02514-7
State	Published - Jan 1 2012
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This material is based on work supported by the National Science Foundation grant DMS-0811041. This publication is based on work partially supported by Award No. KUS-C1-016-04,made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1090/s0025-5718-2011-02514-7

Cite this

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title = "Maximum principle and convergence of central schemes based on slope limiters",

abstract = "A maximum principle and convergence of second order central schemes is proven for scalar conservation laws in dimension one. It is well known that to establish a maximum principle a nonlinear piecewise linear reconstruction is needed and a typical choice is the minmod limiter. Unfortunately, this implies that the scheme uses a first order reconstruction at local extrema. The novelty here is that we allow local nonlinear reconstructions which do not reduce to first order at local extrema and still prove maximum principle and convergence. {\textcopyright} 2011 American Mathematical Society.",

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AU - Popov, Bojan

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AB - A maximum principle and convergence of second order central schemes is proven for scalar conservation laws in dimension one. It is well known that to establish a maximum principle a nonlinear piecewise linear reconstruction is needed and a typical choice is the minmod limiter. Unfortunately, this implies that the scheme uses a first order reconstruction at local extrema. The novelty here is that we allow local nonlinear reconstructions which do not reduce to first order at local extrema and still prove maximum principle and convergence. © 2011 American Mathematical Society.

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ER -

Maximum principle and convergence of central schemes based on slope limiters

Abstract

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