Počet záznamů: 1

Higher-order discrete maximum principle for 1D diffusion-reaction problems

  1. 1.
    0352122 - MU-W 2011 RIV NL eng J - Článek v odborném periodiku
    Vejchodský, Tomáš
    Higher-order discrete maximum principle for 1D diffusion-reaction problems.
    Applied Numerical Mathematics. Roč. 60, č. 4 (2010), s. 486-500 ISSN 0168-9274.
    [Conference in Numerical Analysis (NumAn 2008). Kalamata, 01.09.2008-05.09.2008]
    Grant CEP: GA AV ČR IAA100760702; GA AV ČR(CZ) IAA100190803
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: discrete maximum principle * discrete Green's function * diffusion-reaction problem * higher-order finite element method * hp-FEM * M-matrix
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.919, rok: 2010
    http://www.sciencedirect.com/science/article/pii/S0168927409001731

    Sufficient conditions for the validity of the discrete maximum principle (DMP) for a 1D diffusion-reaction problem -u '' + kappa(2)u = f with homogeneous Dirichlet boundary conditions discretized by the higher-order finite element method are presented. It is proved that the DMP is satisfied if the lengths h of all elements are shorter then one-third of the length of the entire domain and if kappa(2)h(2) is small enough for all elements. In general, the bounds for kappa(2)h(2) depend on the polynomial degree of the elements, on h, and on the size of the domain. The obtained conditions are simple and easy to verify. A technical assumption (nonnegativity of certain rational functions) was verified by computer for polynomial degrees up to 10. The paper contains an analysis of the discrete Green's function which can be of independent interest.
    Trvalý link: http://hdl.handle.net/11104/0191706
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