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    Maximum principle and convergence of central schemes based on slope limiters

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    Type
    Article
    Authors
    Mehmetoglu, Orhan
    Popov, Bojan
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2012-01-01
    Permanent link to this record
    http://hdl.handle.net/10754/598778
    
    Metadata
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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. © 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.
    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).
    Publisher
    American Mathematical Society (AMS)
    Journal
    Mathematics of Computation
    DOI
    10.1090/s0025-5718-2011-02514-7
    ae974a485f413a2113503eed53cd6c53
    10.1090/s0025-5718-2011-02514-7
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