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Maximum principle and convergence of central schemes based on slope limiters


Authors: Orhan Mehmetoglu and Bojan Popov
Journal: Math. Comp. 81 (2012), 219-231
MSC (2010): Primary 65M12; Secondary 65M08
DOI: https://doi.org/10.1090/S0025-5718-2011-02514-7
Published electronically: May 16, 2011
MathSciNet review: 2833493
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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.


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Additional Information

Orhan Mehmetoglu
Affiliation: Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, Texas 77843
Email: omehmet@math.tamu.edu

Bojan Popov
Affiliation: Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, Texas 77843
Email: popov@math.tamu.edu

DOI: https://doi.org/10.1090/S0025-5718-2011-02514-7
Received by editor(s): May 13, 2010
Received by editor(s) in revised form: September 9, 2010, and December 3, 2010
Published electronically: May 16, 2011
Additional Notes: 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)
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.