Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation

Kenta Kobayashi; Takuya Tsuchiya

Applications of Mathematics (2016)

  • Volume: 61, Issue: 2, page 121-133
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Kobayashi, Kenta, and Tsuchiya, Takuya. "Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation." Applications of Mathematics 61.2 (2016): 121-133. <http://eudml.org/doc/276779>.

@article{Kobayashi2016,
abstract = {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.},
author = {Kobayashi, Kenta, Tsuchiya, Takuya},
journal = {Applications of Mathematics},
keywords = {Lagrange interpolation; Babuška-Aziz's technique; difference quotients; Lagrange interpolation; Babuška-Aziz’s technique; difference quotients},
language = {eng},
number = {2},
pages = {121-133},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation},
url = {http://eudml.org/doc/276779},
volume = {61},
year = {2016},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 121
EP - 133
AB - 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.
LA - eng
KW - Lagrange interpolation; Babuška-Aziz's technique; difference quotients; Lagrange interpolation; Babuška-Aziz’s technique; difference quotients
UR - http://eudml.org/doc/276779
ER -

References

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