On third-order limiter functions for finite volume methods

  • Birte Schmidtmann
  • Rémi Abgrall
  • Manuel Torrilhon

DOI: 10.1007/s00574-016-0183-5

Cite this article as:
Schmidtmann, B., Abgrall, R. & Torrilhon, M. Bull Braz Math Soc, New Series (2016) 47: 753. doi:10.1007/s00574-016-0183-5


In this article, we propose a finite volume limiter function for a reconstruction on the three-point stencil. Compared to classical limiter functions in the MUSCL framework, which yield 2nd-order accuracy, the new limiter is 3rd-order accurate for smooth solution. In an earlier work, such a 3rd-order limiter function was proposed and showed successful results [2]. However, it came with unspecified parameters. We close this gap by giving information on these parameters.


non-linear and non-polynomial limiter finite volume hyperbolic conservation laws shock capturing 

Mathematical subject classification

65M08 finite volume methods 

Copyright information

© Sociedade Brasileira de Matemática 2016

Authors and Affiliations

  • Birte Schmidtmann
    • 1
  • Rémi Abgrall
    • 2
  • Manuel Torrilhon
    • 1
  1. 1.Center for Computational Engineering ScienceRWTH Aachen UniversityAachenGermany
  2. 2.Institut für Mathematik & Computational ScienceUniversität ZürichZurichSwitzerland

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