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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F10%3A00352122%21RIV11-AV0-67985840
rdf:type
n17:Vysledek skos:Concept
dcterms: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.
dcterms:title
Higher-order discrete maximum principle for 1D diffusion-reaction problems Higher-order discrete maximum principle for 1D diffusion-reaction problems
skos:prefLabel
Higher-order discrete maximum principle for 1D diffusion-reaction problems Higher-order discrete maximum principle for 1D diffusion-reaction problems
skos:notation
RIV/67985840:_____/10:00352122!RIV11-AV0-67985840
n4:aktivita
n5:Z n5:P
n4:aktivity
P(IAA100190803), P(IAA100760702), Z(AV0Z10190503)
n4:cisloPeriodika
4
n4:dodaniDat
n10:2011
n4:domaciTvurceVysledku
n13:7004974
n4:druhVysledku
n14:J
n4:duvernostUdaju
n18:S
n4:entitaPredkladatele
n15:predkladatel
n4:idSjednocenehoVysledku
261562
n4:idVysledku
RIV/67985840:_____/10:00352122
n4:jazykVysledku
n8:eng
n4:klicovaSlova
discrete maximum principle; discrete Green's function; diffusion-reaction problem; higher-order finite element method; hp-FEM; M-matrix
n4:klicoveSlovo
n9:discrete%20Green%27s%20function n9:hp-FEM n9:M-matrix n9:discrete%20maximum%20principle n9:diffusion-reaction%20problem n9:higher-order%20finite%20element%20method
n4:kodStatuVydavatele
NL - Nizozemsko
n4:kontrolniKodProRIV
[6A3C84C57B81]
n4:nazevZdroje
Applied Numerical Mathematics
n4:obor
n6:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
1
n4:projekt
n7:IAA100190803 n7:IAA100760702
n4:rokUplatneniVysledku
n10:2010
n4:svazekPeriodika
60
n4:tvurceVysledku
Vejchodský, Tomáš
n4:wos
000277031000015
n4:zamer
n16:AV0Z10190503
s:issn
0168-9274
s:numberOfPages
15