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On discrete maximum principles for nonlinear elliptic problems

Author

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  • Karátson, János
  • Korotov, Sergey
  • Křížek, Michal

Abstract

In order to have reliable numerical simulations it is very important to preserve basic qualitative properties of solutions of mathematical models by computed approximations. For scalar second-order elliptic equations, one of such properties is the maximum principle. In our work, we give a short review of the most important results devoted to discrete counterparts of the maximum principle (called discrete maximum principles, DMPs), mainly in the framework of the finite element method, and also present our own recent results on DMPs for a class of second-order nonlinear elliptic problems with mixed boundary conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:76:y:2007:i:1:p:99-108
    DOI: 10.1016/j.matcom.2007.01.011
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    Cited by:

    1. Eduardo Casas & Mariano Mateos, 2012. "Numerical approximation of elliptic control problems with finitely many pointwise constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1319-1343, April.
    2. 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.

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