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On superconvergence properties of Galerkin's method for compact operator equations

On superconvergence properties of Galerkin's method for compact operator equations
On superconvergence properties of Galerkin's method for compact operator equations
Galerkin's method applied to compact operator equations often exhibits superconvergence. In this paper we present a unified framework for an error analysis which deals with the Galerkin and discrete Galerkin methods for equations of the second kind and the eigenvalue problem. An advantage of this framework is that the quadrature errors in the discrete Galerkin method can easily be dealt with. We apply our results to the case of integral equations and spline approximation.
0272-4979
Thomas, K S
b107015f-c7d9-42cc-b87b-207c49e5369a
Spence, A.
4aa5a6e9-27ca-4d04-ae31-e7b67d14adae
Thomas, K S
b107015f-c7d9-42cc-b87b-207c49e5369a
Spence, A.
4aa5a6e9-27ca-4d04-ae31-e7b67d14adae

Thomas, K S and Spence, A. (1983) On superconvergence properties of Galerkin's method for compact operator equations. IMA Journal of Numerical Analysis, 3 (3). (doi:10.1093/imanum/3.3.253).

Record type: Article

Abstract

Galerkin's method applied to compact operator equations often exhibits superconvergence. In this paper we present a unified framework for an error analysis which deals with the Galerkin and discrete Galerkin methods for equations of the second kind and the eigenvalue problem. An advantage of this framework is that the quadrature errors in the discrete Galerkin method can easily be dealt with. We apply our results to the case of integral equations and spline approximation.

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Published date: 1 July 1983
Organisations: Electronic & Software Systems

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Local EPrints ID: 251438
URI: http://eprints.soton.ac.uk/id/eprint/251438
ISSN: 0272-4979
PURE UUID: 42dd5a45-9ae7-40d8-ba9b-35bdaf324dca

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Date deposited: 03 Nov 1999
Last modified: 14 Mar 2024 05:12

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Contributors

Author: K S Thomas
Author: A. Spence

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