Maximum principle and convergence of central schemes based on slope limiters

Type
Article

Authors
Mehmetoglu, Orhan
Popov, Bojan

KAUST Grant Number
KUS-C1-016-04

Date
2012-01-01

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.

Acknowledgements
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

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