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Matrix and Discrete Maximum Principles

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Large-Scale Scientific Computing (LSSC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5910))

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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.

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References

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Author information

Authors and Affiliations

  1. Eötvös Loránd University, Pázmány P. s. 1/c, 1117, Budapest, Hungary

    István Faragó

Authors
  1. István Faragó
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Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads - Building 321, 2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Faragó, I. (2010). Matrix and Discrete Maximum Principles. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_67

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  • DOI: https://doi.org/10.1007/978-3-642-12535-5_67

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12534-8

  • Online ISBN: 978-3-642-12535-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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