Superconvergence of external approximation for two-point boundary problems

Teresa Regińska

Aplikace matematiky (1987)

  • Volume: 32, Issue: 1, page 25-36
  • ISSN: 0862-7940

Abstract

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The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.

How to cite

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Regińska, Teresa. "Superconvergence of external approximation for two-point boundary problems." Aplikace matematiky 32.1 (1987): 25-36. <http://eudml.org/doc/15477>.

@article{Regińska1987,
abstract = {The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.},
author = {Regińska, Teresa},
journal = {Aplikace matematiky},
keywords = {external approximations; superconvergence; external method; Galerkin method; rate of convergence; two-point boundary value problems; external approximations; superconvergence; external method; Galerkin method; rate of convergence},
language = {eng},
number = {1},
pages = {25-36},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Superconvergence of external approximation for two-point boundary problems},
url = {http://eudml.org/doc/15477},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Regińska, Teresa
TI - Superconvergence of external approximation for two-point boundary problems
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 1
SP - 25
EP - 36
AB - The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.
LA - eng
KW - external approximations; superconvergence; external method; Galerkin method; rate of convergence; two-point boundary value problems; external approximations; superconvergence; external method; Galerkin method; rate of convergence
UR - http://eudml.org/doc/15477
ER -

References

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  1. J. P. Aubin, Approximation of elliptic boundary-value problems, Wiley-Interscience, New York, 1972. (1972) Zbl0248.65063MR0478662
  2. C. De Boor B. Swartz, 10.1137/0710052, SIAM J. Numer. Anal. 10 (1973), 582-606. (1973) Zbl0232.65065MR0373328DOI10.1137/0710052
  3. P. Ciarlet, The finite element method for elliptic problems, North-Holland, Publishing Company (1978). (1978) Zbl0383.65058MR0520174
  4. J. Douglas, Jr. T. Dupont, Collocation method for parabolic equations in a single space variable, Lecture Notes in Math., 385 (1974). (1974) MR0483559
  5. J. Douglas, Jr. T. Dupont, Some superconvergence results for Galerkin methods for the approximate solution of two-point boundary problems, - Topics in numerical analysis, ed. J.J.M.F. Miller, pp. 89-92 (1973). (1973) Zbl0277.65052MR0366044
  6. P. J. Davis, Interpolation and approximation, Blaisdell Publishing Company (1963). (1963) Zbl0111.06003MR0157156
  7. M. Křížek P. Neittaanmäki, 10.1007/BF01379664, Numer. Math. 45 (1984), pp. 105-116. (1984) Zbl0575.65104MR0761883DOI10.1007/BF01379664
  8. T. Regińska, 10.1093/imanum/6.3.309, IMA Jour. Numer. Anal. 6 (1986), pp. 309-323. (1986) Zbl0619.65076MR0967671DOI10.1093/imanum/6.3.309
  9. M. Zlámal, Some superconvergence results in the finite element method, - Mathematical Aspects of f.e.m., Lecture Notes 606 (1977), pp. 353 - 362. (1977) MR0488863

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