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 1 2015

Fingerprint

Discrete Maximum Principle
Maximum principle
Finite Element
Nonlinear Elliptic Problems
Interface Conditions
Mixed Boundary Conditions
Finite Element Solution
Banach spaces
Nonlinear Partial Differential Equations
Elliptic Problems
Numerical Scheme
Partial differential equations
Banach space
Boundary conditions
Nonlinearity
Sufficient Conditions
Form

Keywords

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

ASJC Scopus subject areas

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

Cite this

Some discrete maximum principles arising for nonlinear elliptic finite element problems. / Karátson, J.; Korotov, S.

In: Computers and Mathematics with Applications, Vol. 70, No. 11, 01.12.2015, p. 2732-2741.

Research output: Contribution to journalArticle

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