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On a Weak Discrete Maximum Principle for hp-FEM

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    SYSNO ASEP0044977
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JOstatní články
    TitleOn a Weak Discrete Maximum Principle for hp-FEM
    TitleSlabý diskrétní princip maxima pro hp-FEM
    Author(s) Šolín, Pavel (UT-L) RID
    Vejchodský, Tomáš (MU-W) RID, SAI, ORCID
    Source TitleJournal of Computational and Applied Mathematics. - : Elsevier - ISSN 0377-0427
    -, č. 209 (2007), s. 54-65
    Number of pages11 s.
    Languageeng - English
    CountryNL - Netherlands
    Keywordsdiscrete maximum principle ; hp-FEM
    Subject RIVJA - Electronics ; Optoelectronics, Electrical Engineering
    R&D ProjectsGA102/05/0629 GA ČR - Czech Science Foundation (CSF)
    CEZAV0Z20570509 - UE-C, UT-L (2005-2011)
    AV0Z10190503 - MU-W (2005-2011)
    AnnotationIn this paper we prove a new discrete maximum principle (DMP) for the one-dimensional Poisson equation discretized by the hp-FEM. While the DMP for piecewise-linear elements is a classical result from the 1970s, no extensions to hp-FEM have been available to the present day. Due to a negative result by Hoehn and Mittelmann from 1981, related to quadratic Lagrange elements, it was long assumed that higher-order finite elements do not satisfy discrete maximum principles. In this paper we explain why it is not possible to make a straightforward extension of the classical DMP to the higher-order case, and we propose stronger assumptions on the right-hand side under which an extension is possible.
    WorkplaceInstitute of Thermomechanics
    ContactMarie Kajprová,, Tel.: 266 053 154
    Year of Publishing2008