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The Effect of the Consistent Mass Matrix on the Maximum-Principle for Scalar Conservation Equations

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Abstract

In this paper we study the effect of the use of the consistent mass matrix when solving scalar nonlinear conservation equations. It is shown that a continuous finite element method based on artificial viscosity in space and explicit time stepping using the consistent mass matrix cannot satisfy the maximum principle.

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Authors and Affiliations

  1. Department of Mathematics, Texas A& M University, 3368 TAMU, College Station, TX, 77843, USA

    Jean-Luc Guermond & Bojan Popov

  2. Department of Mathematics, Penn State University, University Park, State College, PA, 16802, USA

    Yong Yang

Authors
  1. Jean-Luc Guermond
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  2. Bojan Popov
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  3. Yong Yang
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Corresponding author

Correspondence to Jean-Luc Guermond.

Additional information

This material is based upon work supported in part by the National Science Foundation Grants DMS-1217262, by the Air Force Office of Scientific Research, USAF, under Grant/Contract Number FA9550-15-1-0257, and by the Army Research Office under Grant/Contract Number W911NF-15-1-0517. Draft version, September 7, 2016.

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Guermond, JL., Popov, B. & Yang, Y. The Effect of the Consistent Mass Matrix on the Maximum-Principle for Scalar Conservation Equations. J Sci Comput 70, 1358–1366 (2017). https://doi.org/10.1007/s10915-016-0285-7

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  • DOI: https://doi.org/10.1007/s10915-016-0285-7

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