Maximum principle and convergence of central schemes based on slope limiters

Orhan Mehmetoglu, Bojan Popov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)219-231
Number of pages13
JournalMathematics of Computation
Volume81
Issue number277
DOIs
StatePublished - Jan 1 2012
Externally publishedYes

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