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.
@article{104309, author = {Teresa Regi\'nska}, title = {Error estimates for external approximation of ordinary differential equations and the superconvergence property}, journal = {Applications of Mathematics}, volume = {33}, year = {1988}, pages = {277-290}, zbl = {0664.65076}, mrnumber = {0949249}, language = {en}, url = {http://dml.mathdoc.fr/item/104309} }
Regińska, Teresa. Error estimates for external approximation of ordinary differential equations and the superconvergence property. Applications of Mathematics, Tome 33 (1988) pp. 277-290. http://gdmltest.u-ga.fr/item/104309/
Approximation of elliptic boundary value problems, Wiley-Interscience (1972). (1972) | MR 0478662 | Zbl 0248.65063
Generalized finite element methods: their performance and their relation to mixed methods, SIAM J. Numer. Anal. 20 (1983), 510-536. (1983) | Article | MR 0701094
Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973), 582-606. (1973) | Article | MR 0373328
The finite element method for elliptic problems, North-Holland Publishing Company (1978). (1978) | MR 0520174 | Zbl 0383.65058
Superconvergence for second kind integral equations, Application and Numerical Solution of Integral Equations, Sijthoff, Noordhoff (1980), 103-117. (1980) | MR 0582986
Interpolation and approximation, Blaisdell Publishing Company (1963). (1963)
Some superconvergence results for Galerkin methods for the approximate solution of two point boundary problems, Topics in numerical analysis, (1973), 89-92. (1973) | MR 0366044
Collocation methods for parabolic equations in a single space variable, Lecture Notes in Math. 385 (1974). (1974) | MR 0483559
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. (1976) | Article | MR 0408256
On superconvergence techniques, Acta Appl. Math. 9 (1987), 175-198. (1987) | Article | MR 0900263
Superconvergence of external approximation for two-point boundary problems, Apl. Mat. 32 (1987), pp. 25-36. (1987) | MR 0879327
Superconvergence of piecewise polynomial Galerkin approximations for Fredholm integral equations of the second kind, Numer. Math. 31 (1978), pp. 63-70. (1978) | Article | MR 0508588 | Zbl 0427.65091
On superconvergence properties of Galerkin's method for compact operator equations, IMA J. Numer. Anal. 3 (1983), pp. 253 - 271. (1983) | Article | MR 0723049
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) | MR 0403265
Some superconvergence results in the finite element method, Lecture Notes 606, (1977), p. 353-362. (1977) | MR 0488863