Error estimates for external approximation of ordinary differential equations and the superconvergence property

Teresa Regińska

Aplikace matematiky (1988)

  • Volume: 33, Issue: 4, page 277-290
  • ISSN: 0862-7940

Abstract

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A pointwise error estimate and an estimate in norm are obtained for a class of external methods approximating boundary value problems. Dependence of a superconvergence phenomenon on the external approximation method is studied. In this general framework, superconvergence at the knot points for piecewise polynomial external methods is established.

How to cite

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Regińska, Teresa. "Error estimates for external approximation of ordinary differential equations and the superconvergence property." Aplikace matematiky 33.4 (1988): 277-290. <http://eudml.org/doc/15543>.

@article{Regińska1988,
abstract = {A pointwise error estimate and an estimate in norm are obtained for a class of external methods approximating boundary value problems. Dependence of a superconvergence phenomenon on the external approximation method is studied. In this general framework, superconvergence at the knot points for piecewise polynomial external methods is established.},
author = {Regińska, Teresa},
journal = {Aplikace matematiky},
keywords = {superconvergence; external approximation; pointwise error estimate; finite element subspaces; orthogonal projections; ordinary differential operators; Superconvergence; external approximation; pointwise error estimate; finite element subspaces; orthogonal projections},
language = {eng},
number = {4},
pages = {277-290},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Error estimates for external approximation of ordinary differential equations and the superconvergence property},
url = {http://eudml.org/doc/15543},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Regińska, Teresa
TI - Error estimates for external approximation of ordinary differential equations and the superconvergence property
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 4
SP - 277
EP - 290
AB - A pointwise error estimate and an estimate in norm are obtained for a class of external methods approximating boundary value problems. Dependence of a superconvergence phenomenon on the external approximation method is studied. In this general framework, superconvergence at the knot points for piecewise polynomial external methods is established.
LA - eng
KW - superconvergence; external approximation; pointwise error estimate; finite element subspaces; orthogonal projections; ordinary differential operators; Superconvergence; external approximation; pointwise error estimate; finite element subspaces; orthogonal projections
UR - http://eudml.org/doc/15543
ER -

References

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  1. J. P. Aubin, Approximation of elliptic boundary value problems, Wiley-Interscience (1972). (1972) Zbl0248.65063MR0478662
  2. I. Babuška J. E. Osborn, 10.1137/0720034, SIAM J. Numer. Anal. 20 (1983), 510-536. (1983) Zbl0528.65046MR0701094DOI10.1137/0720034
  3. C. de Boor B. Swartz, 10.1137/0710052, SIAM J. Numer. Anal. 10 (1973), 582-606. (1973) Zbl0232.65065MR0373328DOI10.1137/0710052
  4. P. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Company (1978). (1978) Zbl0383.65058MR0520174
  5. C. A. Chandler, Superconvergence for second kind integral equations, Application and Numerical Solution of Integral Equations, Sijthoff, Noordhoff (1980), 103-117. (1980) Zbl0429.65110MR0582986
  6. P. J. Dams, Interpolation and approximation, Blaisdell Publishing Company (1963). (1963) 
  7. J. Douglas, Jr. T. Dupont, Some superconvergence results for Galerkin methods for the approximate solution of two point boundary problems, Topics in numerical analysis, (1973), 89-92. (1973) Zbl0277.65052MR0366044
  8. J. Douglas, Jr. T. Dupont, Collocation methods for parabolic equations in a single space variable, Lecture Notes in Math. 385 (1974). (1974) MR0483559
  9. T. Dupont, 10.1137/0713032, SIAM J. Numer. Anal. vol. 13, no. 3, (1976), 362-368. (1976) Zbl0332.65050MR0408256DOI10.1137/0713032
  10. M. Křížek P. Neittaanmäki, 10.1007/BF00047538, Acta Appl. Math. 9 (1987), 175-198. (1987) Zbl0624.65107MR0900263DOI10.1007/BF00047538
  11. T. Regińska, Superconvergence of external approximation for two-point boundary problems, Apl. Mat. 32 (1987), pp. 25-36. (1987) Zbl0641.65064MR0879327
  12. G. R. Richter, 10.1007/BF01396014, Numer. Math. 31 (1978), pp. 63-70. (1978) Zbl0427.65091MR0508588DOI10.1007/BF01396014
  13. A. Spence K. S. Thomas, 10.1093/imanum/3.3.253, IMA J. Numer. Anal. 3 (1983), pp. 253 - 271. (1983) Zbl0532.65041MR0723049DOI10.1093/imanum/3.3.253
  14. V. Thomée, Spline approximation and difference schemes for the heat equation. The mathematical foundations of finite element method with application to partial differential equations, Academic Press (1972), pp. 711 - 746. (1972) MR0403265
  15. M. Zlámal, Some superconvergence results in the finite element method, Lecture Notes 606, (1977), p. 353-362. (1977) MR0488863

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