Geodesic
Linear Interpolation on a Tetrahedron
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 80-84
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The standard method for the linear interpolation on a tetrahedron of a function with continuous second-order partial derivatives bounded by a given constant is considered. Estimates of the approximation of first-order derivatives that are more exact than the known estimates are derived.
Mots-clés : multidimensional interpolation
Keywords: finite elements. 
@article{TIMM_2018_24_4_a4,
     author = {N. V. Baidakova},
     title = {Linear {Interpolation} on a {Tetrahedron}},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {80--84},
     year = {2018},
     volume = {24},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a4/}
}
TY  - JOUR
AU  - N. V. Baidakova
TI  - Linear Interpolation on a Tetrahedron
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2018
SP  - 80
EP  - 84
VL  - 24
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a4/
LA  - ru
ID  - TIMM_2018_24_4_a4
ER  - 
%0 Journal Article
%A N. V. Baidakova
%T Linear Interpolation on a Tetrahedron
%J Trudy Instituta matematiki i mehaniki
%D 2018
%P 80-84
%V 24
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a4/
%G ru
%F TIMM_2018_24_4_a4
N. V. Baidakova. Linear Interpolation on a Tetrahedron. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 80-84. http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a4/

[1] Baidakova N.V., “Vliyanie gladkosti na pogreshnost approksimatsii proizvodnykh pri lokalnoi interpolyatsii na triangulyatsiyakh”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17:3 (2011), 83–97

[2] Baidakova N.V., “Ob otsenkakh P. Zhame dlya konechnykh elementov s interpolyatsiei v ravnomernykh uzlakh simpleksa”, Mat. tr., 20:1 (2017), 43–74 | MR | Zbl

[3] Klyachin V.A., “Modifitsirovannoe uslovie pustoi sfery Delone v zadache approksimatsii gradienta”, Izv. RAN. Ser. matematicheskaya, 80:3 (2016), 95–102 | DOI | MR | Zbl

[4] Subbotin Yu.N., “Zavisimost otsenok mnogomernoi kusochno polinomialnoi approksimatsii ot geometricheskikh kharakteristik triangulyatsii”, Tr. MIAN SSSR, 189, 1989, 117–137

[5] Ciarlet P.G., Raviart P.A., “General Lagrange and Hermite interpolation in $R^n$ with applications to finite element methods”, Arch. Rational Mech. Anal., 46:3 (1972), 177–199 | DOI | MR | Zbl

[6] Hannukainen A., Korotov S., Kr̂íẑek M., “On Synge-type angle condition for d-simplices”, Appl. Math., 62:1 (2017), 1–13 | DOI | MR | Zbl

[7] Jamet P., “Estimation d'erreur pour des éléments finis droits presque dégénérés”, RAIRO Anal. Numer., 10:1 (1976), 43–60 | MR | Zbl