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

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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

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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 = {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 - local interpolation; quadratic Lagrange finite element; error estimation
UR - http://eudml.org/doc/249800
ER -

References

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  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${}^{ie}$, 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

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