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

Result code in IS VaVaI
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Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Higher-order discrete maximum principle for 1D diffusion-reaction problems
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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