Maximum principle and convergence of central schemes based on slope limiters

Mehmetoglu, Orhan; Popov, Bojan

doi:10.1090/S0025-5718-2011-02514-7

Maximum principle and convergence of central schemes based on slope limiters
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by Orhan Mehmetoglu and Bojan Popov;

Math. Comp. 81 (2012), 219-231

DOI: https://doi.org/10.1090/S0025-5718-2011-02514-7

Published electronically: May 16, 2011

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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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