| Title:
|
Error estimates for external approximation of ordinary differential equations and the superconvergence property (English) |
| Author:
|
Regińska, Teresa |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1988 |
| Pages:
|
277-290 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
superconvergence |
| Keyword:
|
external approximation |
| Keyword:
|
pointwise error estimate |
| Keyword:
|
finite element subspaces |
| Keyword:
|
orthogonal projections |
| Keyword:
|
ordinary differential operators |
| MSC:
|
34B05 |
| MSC:
|
65L10 |
| idZBL:
|
Zbl 0664.65076 |
| idMR:
|
MR0949249 |
| DOI:
|
10.21136/AM.1988.104309 |
| . |
| Date available:
|
2008-05-20T18:34:54Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104309 |
| . |
| Reference:
|
[1] J. P. Aubin: Approximation of elliptic boundary value problems.Wiley-Interscience (1972). Zbl 0248.65063, MR 0478662 |
| Reference:
|
[2] I. Babuška J. E. Osborn: Generalized finite element methods: their performance and their relation to mixed methods.SIAM J. Numer. Anal. 20 (1983), 510-536. MR 0701094, 10.1137/0720034 |
| Reference:
|
[3] C. de Boor B. Swartz: Collocation at Gaussian points.SIAM J. Numer. Anal. 10 (1973), 582-606. MR 0373328, 10.1137/0710052 |
| Reference:
|
[4] P. Ciarlet: The finite element method for elliptic problems.North-Holland Publishing Company (1978). Zbl 0383.65058, MR 0520174 |
| Reference:
|
[5] C. A. Chandler: Superconvergence for second kind integral equations, Application and Numerical Solution of Integral Equations.Sijthoff, Noordhoff (1980), 103-117. MR 0582986 |
| Reference:
|
[6] P. J. Dams: Interpolation and approximation.Blaisdell Publishing Company (1963). |
| Reference:
|
[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. MR 0366044 |
| Reference:
|
[8] J. Douglas, Jr. T. Dupont: Collocation methods for parabolic equations in a single space variable.Lecture Notes in Math. 385 (1974). MR 0483559 |
| Reference:
|
[9] T. Dupont: A unified theory of superconvergence for Galerkin methods for two-point boundary value problems.SIAM J. Numer. Anal. vol. 13, no. 3, (1976), 362-368. MR 0408256, 10.1137/0713032 |
| Reference:
|
[10] M. Křížek P. Neittaanmäki: On superconvergence techniques.Acta Appl. Math. 9 (1987), 175-198. MR 0900263, 10.1007/BF00047538 |
| Reference:
|
[11] T. Regińska: Superconvergence of external approximation for two-point boundary problems.Apl. Mat. 32 (1987), pp. 25-36. MR 0879327 |
| Reference:
|
[12] G. R. Richter: Superconvergence of piecewise polynomial Galerkin approximations for Fredholm integral equations of the second kind.Numer. Math. 31 (1978), pp. 63-70. Zbl 0427.65091, MR 0508588, 10.1007/BF01396014 |
| Reference:
|
[13] A. Spence K. S. Thomas: On superconvergence properties of Galerkin's method for compact operator equations.IMA J. Numer. Anal. 3 (1983), pp. 253 - 271. MR 0723049, 10.1093/imanum/3.3.253 |
| Reference:
|
[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. MR 0403265 |
| Reference:
|
[15] M. Zlámal: Some superconvergence results in the finite element method.Lecture Notes 606, (1977), p. 353-362. MR 0488863, 10.1007/BFb0064473 |
| . |
