N -widths for singularly perturbed problems

Martin Stynes; R. Bruce Kellogg

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 343-352
  • ISSN: 0862-7959

Abstract

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Kolmogorov N -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the N -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.

How to cite

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Stynes, Martin, and Kellogg, R. Bruce. "$N$-widths for singularly perturbed problems." Mathematica Bohemica 127.2 (2002): 343-352. <http://eudml.org/doc/249065>.

@article{Stynes2002,
abstract = {Kolmogorov $N$-widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the $N$-widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.},
author = {Stynes, Martin, Kellogg, R. Bruce},
journal = {Mathematica Bohemica},
keywords = {$N$-width; singularly perturbed; differential equation; boundary value problem; convection-diffusion; reaction-diffusion; -width; singularly perturbed; differential equation; boundary value problem; convection-diffusion; reaction-diffusion},
language = {eng},
number = {2},
pages = {343-352},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$N$-widths for singularly perturbed problems},
url = {http://eudml.org/doc/249065},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Stynes, Martin
AU - Kellogg, R. Bruce
TI - $N$-widths for singularly perturbed problems
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 343
EP - 352
AB - Kolmogorov $N$-widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the $N$-widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
LA - eng
KW - $N$-width; singularly perturbed; differential equation; boundary value problem; convection-diffusion; reaction-diffusion; -width; singularly perturbed; differential equation; boundary value problem; convection-diffusion; reaction-diffusion
UR - http://eudml.org/doc/249065
ER -

References

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  9. On N -widths for elliptic problems, J. Math. Anal. Appl. 247 (2000), 272–289. (2000) Zbl0963.35047MR1766938
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  11. N -Widths in Approximation Theory, Springer, Berlin, 1985. (1985) Zbl0551.41001MR0774404
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  13. Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems I: reaction-diffusion-type problems, IMA J. Numer. Anal. 15 (1995), 117–139. (1995) MR1311341

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