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Discrete maximum principle for parabolic problems solved by prismatic finite elements

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  • Vejchodský, Tomáš
  • Korotov, Sergey
  • Hannukainen, Antti

Abstract

In this paper we analyze the discrete maximum principle (DMP) for a non-stationary diffusion–reaction problem solved by means of prismatic finite elements and θ-method. We derive geometric conditions on the shape parameters of prismatic partitions and time-steps which a priori guarantee validity of the DMP. The presented numerical tests illustrate the sharpness of the obtained conditions.

Suggested Citation

  • Vejchodský, Tomáš & Korotov, Sergey & Hannukainen, Antti, 2010. "Discrete maximum principle for parabolic problems solved by prismatic finite elements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(8), pages 1758-1770.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:8:p:1758-1770
    DOI: 10.1016/j.matcom.2009.10.001
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    References listed on IDEAS

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    1. Karátson, János & Korotov, Sergey & Křížek, Michal, 2007. "On discrete maximum principles for nonlinear elliptic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 99-108.
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