Geodesic
Error estimates for external approximation of ordinary differential equations and the superconvergence property
Applications of Mathematics, Tome 33 (1988) no. 4, pp. 277-290
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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.
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.
DOI : 10.21136/AM.1988.104309
Classification : 34B05, 65L10
Keywords: superconvergence; external approximation; pointwise error estimate; finite element subspaces; orthogonal projections; ordinary differential operators 
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Regińska, Teresa. Error estimates for external approximation of ordinary differential equations and the superconvergence property. Applications of Mathematics, Tome 33 (1988) no. 4, pp. 277-290. doi: 10.21136/AM.1988.104309

[1] J. P. Aubin: Approximation of elliptic boundary value problems. Wiley-Interscience (1972). | MR | Zbl

[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. | DOI | MR

[3] C. de Boor B. Swartz: Collocation at Gaussian points. SIAM J. Numer. Anal. 10 (1973), 582-606. | DOI | MR

[4] P. Ciarlet: The finite element method for elliptic problems. North-Holland Publishing Company (1978). | MR | Zbl

[5] C. A. Chandler: Superconvergence for second kind integral equations, Application and Numerical Solution of Integral Equations. Sijthoff, Noordhoff (1980), 103-117. | MR

[6] P. J. Dams: Interpolation and approximation. Blaisdell Publishing Company (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. | MR

[8] J. Douglas, Jr. T. Dupont: Collocation methods for parabolic equations in a single space variable. Lecture Notes in Math. 385 (1974). | MR

[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. | DOI | MR

[10] M. Křížek P. Neittaanmäki: On superconvergence techniques. Acta Appl. Math. 9 (1987), 175-198. | DOI | MR

[11] T. Regińska: Superconvergence of external approximation for two-point boundary problems. Apl. Mat. 32 (1987), pp. 25-36. | MR

[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. | DOI | MR | Zbl

[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. | DOI | MR

[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

[15] M. Zlámal: Some superconvergence results in the finite element method. Lecture Notes 606, (1977), p. 353-362. | DOI | MR

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