Local interpolation by a quadratic Lagrange finite element in 1D

Josef Dalík

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 2, page 103-114
  • ISSN: 0044-8753

Abstract

top
We analyse the error of interpolation of functions from the space H 3 ( a , c ) in the nodes a < b < c of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes a , b , c change as the length of interval [ a , c ] approaches zero.

How to cite

top

Dalík, Josef. "Local interpolation by a quadratic Lagrange finite element in 1D." Archivum Mathematicum 042.2 (2006): 103-114. <http://eudml.org/doc/249800>.

@article{Dalík2006,
abstract = {We analyse the error of interpolation of functions from the space $H^3(a,c)$ in the nodes $a<b<c$ of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes $a,b,c$ change as the length of interval $[a,c]$ approaches zero.},
author = {Dalík, Josef},
journal = {Archivum Mathematicum},
keywords = {quadratic Lagrange finite elements in 1D; local interpolation of functions in one variable; local interpolation; quadratic Lagrange finite element; error estimation},
language = {eng},
number = {2},
pages = {103-114},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Local interpolation by a quadratic Lagrange finite element in 1D},
url = {http://eudml.org/doc/249800},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Dalík, Josef
TI - Local interpolation by a quadratic Lagrange finite element in 1D
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 2
SP - 103
EP - 114
AB - We analyse the error of interpolation of functions from the space $H^3(a,c)$ in the nodes $a<b<c$ of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes $a,b,c$ change as the length of interval $[a,c]$ approaches zero.
LA - eng
KW - quadratic Lagrange finite elements in 1D; local interpolation of functions in one variable; local interpolation; quadratic Lagrange finite element; error estimation
UR - http://eudml.org/doc/249800
ER -

References

top
  1. Hutson V. C. L., Pym J. S., Applications of Functional Analysis and Operator Theory, Academic Press, London, 1980. (1980) Zbl0426.46009MR0569354
  2. Křížek M., Neittaanmäki P., Finite Element Approximation of Variational Problems and Applications, Longman Scientific & Technical, Essex, 1990. (1990) Zbl0708.65106MR1066462
  3. Nečas J., Les méthodes directes en théorie des équations elliptiques, Masson et C, Éditeurs, Paris; Academia, Éditeurs, Prague, 1967. (1967) MR0227584
  4. Rudin W., Principles of Mathematical Analysis, McGraw-Hill, New York, 1964. (1964) Zbl0148.02903MR0166310
  5. Strang G., Fix G. J., An Analysis of the Finite Element Method, Prentice Hall, Englewood Clifs, N. J., 1973. (1973) Zbl0356.65096MR0443377
  6. Ženíšek A., Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations, Academic Press, London, 1990. (1990) MR1086876

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.