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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Maximum principle and convergence of central schemes based on slope limiters
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by Orhan Mehmetoglu and Bojan Popov PDF
Math. Comp. 81 (2012), 219-231 Request permission


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:
  • Bojan Popov
  • Affiliation: Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, Texas 77843
  • Email:
  • 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)
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 219-231
  • MSC (2010): Primary 65M12; Secondary 65M08
  • DOI:
  • MathSciNet review: 2833493