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

Aplikace matematiky (1988)

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

## Access Full Article

top## Abstract

top## How to cite

topRegińska, 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

top- J. P. Aubin, Approximation of elliptic boundary value problems, Wiley-Interscience (1972). (1972) Zbl0248.65063MR0478662
- I. Babuška J. E. Osborn, 10.1137/0720034, SIAM J. Numer. Anal. 20 (1983), 510-536. (1983) Zbl0528.65046MR0701094DOI10.1137/0720034
- C. de Boor B. Swartz, 10.1137/0710052, SIAM J. Numer. Anal. 10 (1973), 582-606. (1973) Zbl0232.65065MR0373328DOI10.1137/0710052
- P. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Company (1978). (1978) Zbl0383.65058MR0520174
- C. A. Chandler, Superconvergence for second kind integral equations, Application and Numerical Solution of Integral Equations, Sijthoff, Noordhoff (1980), 103-117. (1980) Zbl0429.65110MR0582986
- P. J. Dams, Interpolation and approximation, Blaisdell Publishing Company (1963). (1963)
- 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
- J. Douglas, Jr. T. Dupont, Collocation methods for parabolic equations in a single space variable, Lecture Notes in Math. 385 (1974). (1974) MR0483559
- T. Dupont, 10.1137/0713032, SIAM J. Numer. Anal. vol. 13, no. 3, (1976), 362-368. (1976) Zbl0332.65050MR0408256DOI10.1137/0713032
- M. Křížek P. Neittaanmäki, 10.1007/BF00047538, Acta Appl. Math. 9 (1987), 175-198. (1987) Zbl0624.65107MR0900263DOI10.1007/BF00047538
- T. Regińska, Superconvergence of external approximation for two-point boundary problems, Apl. Mat. 32 (1987), pp. 25-36. (1987) Zbl0641.65064MR0879327
- G. R. Richter, 10.1007/BF01396014, Numer. Math. 31 (1978), pp. 63-70. (1978) Zbl0427.65091MR0508588DOI10.1007/BF01396014
- 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
- 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
- M. Zlámal, Some superconvergence results in the finite element method, Lecture Notes 606, (1977), p. 353-362. (1977) MR0488863

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.