# Superconvergence of external approximation for two-point boundary problems

Aplikace matematiky (1987)

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

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topRegińska, 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

top- J. P. Aubin, Approximation of elliptic boundary-value problems, Wiley-Interscience, New York, 1972. (1972) Zbl0248.65063MR0478662
- 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
- J. Douglas, Jr. T. Dupont, Collocation method for parabolic equations in a single space variable, Lecture Notes in Math., 385 (1974). (1974) MR0483559
- 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
- P. J. Davis, Interpolation and approximation, Blaisdell Publishing Company (1963). (1963) Zbl0111.06003MR0157156
- M. Křížek P. Neittaanmäki, 10.1007/BF01379664, Numer. Math. 45 (1984), pp. 105-116. (1984) Zbl0575.65104MR0761883DOI10.1007/BF01379664
- 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
- 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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