Some discrete maximum principles arising for nonlinear elliptic finite element problems

J. Karátson, S. Korotov

Research output: Contribution to journalArticle

Abstract

The discrete maximum principle (DMP) is an important measure of the qualitative reliability of the applied numerical scheme for elliptic problems. This paper starts with formulating simple sufficient conditions for the matrix case and for nonlinear forms in Banach spaces. Then a DMP is derived for finite element solutions for certain nonlinear partial differential equations: we address nonlinear elliptic problems with mixed boundary conditions and interface conditions, allowing possibly degenerate nonlinearities and thus extending our previous results.

Original languageEnglish
Pages (from-to)2732-2741
Number of pages10
JournalComputers and Mathematics with Applications
Volume70
Issue number11
DOIs
Publication statusPublished - Dec 2015

Keywords

  • Discrete maximum principle
  • Finite element method
  • Nonlinear elliptic problem

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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