On discrete maximum principles for nonlinear elliptic problems

János Karátson, Sergey Korotov and Michal Křížek

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 76, issue 1, 99-108

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.

Keywords: Nonlinear elliptic problem; Mixed boundary conditions; Discrete maximum principle; Finite element method; Quadratures (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:76:y:2007:i:1:p:99-108

DOI: 10.1016/j.matcom.2007.01.011

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