Geodesic
A priori error estimates for Lagrange interpolation on triangles
Applications of Mathematics, Tome 60 (2015) no. 5, pp. 485-499.

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

We present the error analysis of Lagrange interpolation on triangles. A new a priori error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed in order to get this type of error estimates. To derive the new error estimate, we make use of the two key observations. The first is that squeezing a right isosceles triangle perpendicularly does not reduce the approximation property of Lagrange interpolation. An arbitrary triangle is obtained from a squeezed right triangle by a linear transformation. The second key observation is that the ratio of the singular values of the linear transformation is bounded by the circumradius of the target triangle.
DOI : 10.1007/s10492-015-0108-4
Classification : 65D05, 65N30
Keywords: finite element method; Lagrange interpolation; circumradius condition; minimum angle condition; maximum angle condition 
@article{10_1007_s10492_015_0108_4,
     author = {Kobayashi, Kenta and Tsuchiya, Takuya},
     title = {A priori error estimates for {Lagrange} interpolation on triangles},
     journal = {Applications of Mathematics},
     pages = {485--499},
     publisher = {mathdoc},
     volume = {60},
     number = {5},
     year = {2015},
     doi = {10.1007/s10492-015-0108-4},
     mrnumber = {3396477},
     zbl = {06486922},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0108-4/}
}
TY  - JOUR
AU  - Kobayashi, Kenta
AU  - Tsuchiya, Takuya
TI  - A priori error estimates for Lagrange interpolation on triangles
JO  - Applications of Mathematics
PY  - 2015
SP  - 485
EP  - 499
VL  - 60
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0108-4/
DO  - 10.1007/s10492-015-0108-4
LA  - en
ID  - 10_1007_s10492_015_0108_4
ER  - 
%0 Journal Article
%A Kobayashi, Kenta
%A Tsuchiya, Takuya
%T A priori error estimates for Lagrange interpolation on triangles
%J Applications of Mathematics
%D 2015
%P 485-499
%V 60
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0108-4/
%R 10.1007/s10492-015-0108-4
%G en
%F 10_1007_s10492_015_0108_4
Kobayashi, Kenta; Tsuchiya, Takuya. A priori error estimates for Lagrange interpolation on triangles. Applications of Mathematics, Tome 60 (2015) no. 5, pp. 485-499. doi : 10.1007/s10492-015-0108-4. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0108-4/

Cité par Sources :