Geodesic
An algorithm for constructing a finite element of the third degree
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 799-814 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article presents an algorithm of setting Hermite interpolation conditions in tetrahedra of triangulated area in order to obtain a continuous piecewise-polynomial function. The use of the obtained finite element space requires additional restrictions on triangulation as compared with the space under construction using Lagrange interpolation, but the obtained finite element space has a smaller dimension.
Mots-clés : multidimensional interpolation
Keywords: finite elements. 
@article{SEMR_2016_13_a98,
     author = {N. V. Baidakova},
     title = {An algorithm for constructing a finite element of the third degree},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {799--814},
     year = {2016},
     volume = {13},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a98/}
}
TY  - JOUR
AU  - N. V. Baidakova
TI  - An algorithm for constructing a finite element of the third degree
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2016
SP  - 799
EP  - 814
VL  - 13
UR  - http://geodesic.mathdoc.fr/item/SEMR_2016_13_a98/
LA  - ru
ID  - SEMR_2016_13_a98
ER  - 
%0 Journal Article
%A N. V. Baidakova
%T An algorithm for constructing a finite element of the third degree
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2016
%P 799-814
%V 13
%U http://geodesic.mathdoc.fr/item/SEMR_2016_13_a98/
%G ru
%F SEMR_2016_13_a98
N. V. Baidakova. An algorithm for constructing a finite element of the third degree. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 799-814. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a98/

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

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

[3] Yu. N. Subbotin, “The dependence of estimates of a multidimensional piecewise-polynomial approximation on the geometric characteristics of a triangulation”, Trudy Mat. Inst. Steklov, 189, 1989, 117–137 | MR

[4] M. Kr̆íz̆ek, “On the maximum angle condition for linear tetrahedral elements”, SIAM J. Numer. Anal., 29 (1992), 513–520 | DOI | MR

[5] A. Rand, “Average interpolation under the maximum angle condition”, SIAM J. Numer. Anal., 50 (2012), 2538–2559 | DOI | MR | Zbl

[6] A. Ženišek, J. Hoderova-Zlamalova, “Semiregular Hermite tetrahedral finite elements”, Appl. of Math., 4 (2001), 295–315 | MR | Zbl

[7] N. V. Baidakova, “On some interpolation third-degree plynomials on a three-dimensional simplex”, Trudy Inst. Mat. Mekh. UrO RAN, 14, 2008, 43–57 | MR