Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles

Josef Dalík

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 4, page 285-297
  • ISSN: 0044-8753

Abstract

top
An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple a 1 , ⋯ , a 6 of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: a 1 , ⋯ , a 6 are the vertices of triangles T 1 , ⋯ , T 4 without obtuse inner angles such that T 1 has one side common with T j for j = 2 , 3 , 4 .

How to cite

top

Dalík, Josef. "Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles." Archivum Mathematicum 035.4 (1999): 285-297. <http://eudml.org/doc/248358>.

@article{Dalík1999,
abstract = {An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple $a^1,\dots ,a^6$ of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: $a^1,\dots ,a^6$ are the vertices of triangles $T_1,\dots ,T_4$ without obtuse inner angles such that $T_1$ has one side common with $T_j$ for $j=2,3,4$.},
author = {Dalík, Josef},
journal = {Archivum Mathematicum},
keywords = {quadratic Lagrange interpolation in 2D; stability; quadratic Lagrange interpolation in 2D; Lagrange basis function stability; error bounds},
language = {eng},
number = {4},
pages = {285-297},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles},
url = {http://eudml.org/doc/248358},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Dalík, Josef
TI - Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 4
SP - 285
EP - 297
AB - An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple $a^1,\dots ,a^6$ of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: $a^1,\dots ,a^6$ are the vertices of triangles $T_1,\dots ,T_4$ without obtuse inner angles such that $T_1$ has one side common with $T_j$ for $j=2,3,4$.
LA - eng
KW - quadratic Lagrange interpolation in 2D; stability; quadratic Lagrange interpolation in 2D; Lagrange basis function stability; error bounds
UR - http://eudml.org/doc/248358
ER -

References

top
  1. Quadratic interpolation polynomials in vertices of strongly regular triangulations, in Finite Element Methods, superconvergence, post-processing and a posteriori estimates, Ed. Křižek, Neittaanmäki, Stenberg, Marcel Dekker (1996), 85–95. (1996) MR1602833
  2. On multivariate Lagrange interpolation, Math. of Comp. 64 (1995), 1147–1170. (1995) MR1297477

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.