Geodesic
Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation
Applications of Mathematics, Tome 61 (2016) no. 2, pp. 121-133.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We consider the error analysis of Lagrange interpolation on triangles and tetrahedrons. For Lagrange interpolation of order one, Babuška and Aziz showed that squeezing a right isosceles triangle perpendicularly does not deteriorate the optimal approximation order. We extend their technique and result to higher-order Lagrange interpolation on both triangles and tetrahedrons. To this end, we make use of difference quotients of functions with two or three variables. Then, the error estimates on squeezed triangles and tetrahedrons are proved by a method that is a straightforward extension of the original one given by Babuška-Aziz.
DOI : 10.1007/s10492-016-0125-y
Classification : 65D05, 65N30
Keywords: Lagrange interpolation; Babuška-Aziz's technique; difference quotients 
@article{10_1007_s10492_016_0125_y,
     author = {Kobayashi, Kenta and Tsuchiya, Takuya},
     title = {Extending {Babu\v{s}ka-Aziz's} theorem to higher-order {Lagrange} interpolation},
     journal = {Applications of Mathematics},
     pages = {121--133},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {2016},
     doi = {10.1007/s10492-016-0125-y},
     mrnumber = {3470770},
     zbl = {06562150},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0125-y/}
}
TY  - JOUR
AU  - Kobayashi, Kenta
AU  - Tsuchiya, Takuya
TI  - Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation
JO  - Applications of Mathematics
PY  - 2016
SP  - 121
EP  - 133
VL  - 61
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0125-y/
DO  - 10.1007/s10492-016-0125-y
LA  - en
ID  - 10_1007_s10492_016_0125_y
ER  - 
%0 Journal Article
%A Kobayashi, Kenta
%A Tsuchiya, Takuya
%T Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation
%J Applications of Mathematics
%D 2016
%P 121-133
%V 61
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0125-y/
%R 10.1007/s10492-016-0125-y
%G en
%F 10_1007_s10492_016_0125_y
Kobayashi, Kenta; Tsuchiya, Takuya. Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation. Applications of Mathematics, Tome 61 (2016) no. 2, pp. 121-133. doi : 10.1007/s10492-016-0125-y. http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0125-y/

Cité par Sources :