On discrete maximum principles for nonlinear elliptic problems

J. Karátson, Sergey Korotov, Michal Křížek

Research output: Contribution to journalArticle

34 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)99-108
Number of pages10
JournalMathematics and Computers in Simulation
Volume76
Issue number1-3
DOIs
Publication statusPublished - Oct 12 2007

Fingerprint

Discrete Maximum Principle
Nonlinear Elliptic Problems
Maximum principle
Maximum Principle
Second Order Elliptic Equations
Mixed Boundary Conditions
Qualitative Properties
Finite Element Method
Scalar
Mathematical Model
Numerical Simulation
Approximation
Boundary conditions
Mathematical models
Finite element method
Computer simulation
Class
Framework
Review

Keywords

  • Discrete maximum principle
  • Finite element method
  • Mixed boundary conditions
  • Nonlinear elliptic problem
  • Quadratures

ASJC Scopus subject areas

  • Information Systems and Management
  • Control and Systems Engineering
  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

On discrete maximum principles for nonlinear elliptic problems. / Karátson, J.; Korotov, Sergey; Křížek, Michal.

In: Mathematics and Computers in Simulation, Vol. 76, No. 1-3, 12.10.2007, p. 99-108.

Research output: Contribution to journalArticle

Karátson, J. ; Korotov, Sergey ; Křížek, Michal. / On discrete maximum principles for nonlinear elliptic problems. In: Mathematics and Computers in Simulation. 2007 ; Vol. 76, No. 1-3. pp. 99-108.
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