Error estimates for some quasi-interpolation operators

Rüdiger Verfürth

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 4, page 695-713
  • ISSN: 0764-583X

How to cite

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Verfürth, Rüdiger. "Error estimates for some quasi-interpolation operators." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.4 (1999): 695-713. <http://eudml.org/doc/193941>.

@article{Verfürth1999,
author = {Verfürth, Rüdiger},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {error bounds; quasi-interpolation operators; Clément-operator; a posteriori error estimates; nodal interpolation operator},
language = {eng},
number = {4},
pages = {695-713},
publisher = {Dunod},
title = {Error estimates for some quasi-interpolation operators},
url = {http://eudml.org/doc/193941},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Verfürth, Rüdiger
TI - Error estimates for some quasi-interpolation operators
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 4
SP - 695
EP - 713
LA - eng
KW - error bounds; quasi-interpolation operators; Clément-operator; a posteriori error estimates; nodal interpolation operator
UR - http://eudml.org/doc/193941
ER -

References

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  1. [1] Handbook of Mathematical Functions, M. Abramowitz and I.A. Stegun Eds., Dover Publ., New York (1965). 
  2. [2] R.A. Adams, Sobolev Spaces. Academic Press, NewYork (1975). Zbl0314.46030MR450957
  3. [3] L. Angermann, A posteriori Fehlerabschätzungen für Lösungen gestörter Operatorgleichungen. Habilitationsschrift, Universität Erlangen-Nürnberg (1994). 
  4. [4] J.H. Bramble and L.E. Payne, Bounds in the Neumann problem for second order uniformly elliptic operators. Pacific J. Math.12 (1962) 823-833. Zbl0111.09701MR146504
  5. [5] C. Carstensen and St. A. Punken, Constants in Clément-interpolation error and residual based a posteriori error estimates in finite element methods. Report 97-11, Universität Kiel (1997). Zbl0973.65091
  6. [6] Ph.G. Ciarlet, The Finite Element Method for Elliptic Problems. North Holland (1978). Zbl0383.65058MR520174
  7. [7] P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84. Zbl0368.65008MR400739
  8. [8] R.G. Durán, On polynomial approximation in Sobolev spaces. SIAM J. Numer. Anal. 20 (1983) 985-988. Zbl0523.41020MR714693
  9. [9] L.E. Payne and H.F. Weinberger, An optimal Poincaré-inequality for convex domains. Arch. Rational Mech. Anal. 5 (1960) 286-292. Zbl0099.08402MR117419
  10. [10] L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483-493. Zbl0696.65007MR1011446
  11. [11] R. Verfürth, A Review of a posteriori Error Estimation and adaptive Mesh-Refinement Techniques. Teubner-Wiley, Stuttgart (1996). Zbl0853.65108

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