Maximum principle and convergence of central schemes based on slope limiters

Handle URI:
http://hdl.handle.net/10754/598778
Title:
Maximum principle and convergence of central schemes based on slope limiters
Authors:
Mehmetoglu, Orhan; Popov, Bojan
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.
Citation:
Mehmetoglu O, Popov B (2012) Maximum principle and convergence of central schemes based on slope limiters. Math Comp 81: 219–231. Available: http://dx.doi.org/10.1090/s0025-5718-2011-02514-7.
Publisher:
American Mathematical Society (AMS)
Journal:
Mathematics of Computation
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
1-Jan-2012
DOI:
10.1090/s0025-5718-2011-02514-7
Type:
Article
ISSN:
0025-5718; 1088-6842
Sponsors:
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMehmetoglu, Orhanen
dc.contributor.authorPopov, Bojanen
dc.date.accessioned2016-02-25T13:41:02Zen
dc.date.available2016-02-25T13:41:02Zen
dc.date.issued2012-01-01en
dc.identifier.citationMehmetoglu O, Popov B (2012) Maximum principle and convergence of central schemes based on slope limiters. Math Comp 81: 219–231. Available: http://dx.doi.org/10.1090/s0025-5718-2011-02514-7.en
dc.identifier.issn0025-5718en
dc.identifier.issn1088-6842en
dc.identifier.doi10.1090/s0025-5718-2011-02514-7en
dc.identifier.urihttp://hdl.handle.net/10754/598778en
dc.description.abstractA 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.en
dc.description.sponsorshipThis 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).en
dc.publisherAmerican Mathematical Society (AMS)en
dc.titleMaximum principle and convergence of central schemes based on slope limitersen
dc.typeArticleen
dc.identifier.journalMathematics of Computationen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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