Matrix and discrete maximum principles

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Qualitative properties play central role in constructing reliable numerical models for parabolic problems. One of such basic properties is the discrete maximum principle. In this paper we analyze its relation to the so-called matrix maximum principles. We analyze the different matrix maximum principles (Ciarlet, Stoyan and Ciarlet-Stoyan maximum principles) and their relation. Introducing the iterative algebraic problem (IAP) we show that the discrete maximum principles for discrete parabolic problems are more general than the algebraic maximum principles. We also analyze and compare the conditions which ensure the above qualitative properties.

Original languageEnglish
Title of host publicationLarge-Scale Scientific Computing - 7th International Conference, LSSC 2009, Revised Papers
Pages563-570
Number of pages8
DOIs
Publication statusPublished - Jun 25 2010
Event7th International Conference on Large-Scale Scientific Computations, LSSC 2009 - Sozopol, Bulgaria
Duration: Jun 4 2009Jun 8 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5910 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Conference on Large-Scale Scientific Computations, LSSC 2009
CountryBulgaria
CitySozopol
Period6/4/096/8/09

Keywords

  • Discrete maximum principle
  • Finite difference method
  • Heat equation
  • Linear finite element
  • Qualitative properties

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Faragó, I. (2010). Matrix and discrete maximum principles. In Large-Scale Scientific Computing - 7th International Conference, LSSC 2009, Revised Papers (pp. 563-570). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5910 LNCS). https://doi.org/10.1007/978-3-642-12535-5_67