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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. 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. (en)
Title	Higher-order discrete maximum principle for 1D diffusion-reaction problems Higher-order discrete maximum principle for 1D diffusion-reaction problems (en)
skos:prefLabel	Higher-order discrete maximum principle for 1D diffusion-reaction problems Higher-order discrete maximum principle for 1D diffusion-reaction problems (en)
skos:notation	RIV/67985840:_____/10:00352122!RIV11-AV0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100190803), P(IAA100760702), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Vejchodský, Tomáš
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	261562
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/10:00352122
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	discrete maximum principle; discrete Green's function; diffusion-reaction problem; higher-order finite element method; hp-FEM; M-matrix (en)
http://linked.open.../riv/klicoveSlovo	discrete Green's function M-matrix higher-order finite element method hp-FEM diffusion-reaction problem discrete maximum principle
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[6A3C84C57B81]
http://linked.open...i/riv/nazevZdroje	Applied Numerical Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Methods of higher order of accuracy for solution of multi-physics coupled problems The finite element method for higher dimensional problems
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	60
http://linked.open...iv/tvurceVysledku	Vejchodský, Tomáš
http://linked.open...ain/vavai/riv/wos	000277031000015
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0168-9274
number of pages	15 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Higher-order discrete maximum principle for 1D diffusion-reaction problems Higher-order discrete maximum principle for 1D diffusion-reaction problems Higher-order discrete maximum principle for 1D diffusion-reaction problems

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