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A superconvergence result for solutions of compact operator equations

Published online by Cambridge University Press:  17 April 2009

Rekha P. Kulkarni
Rekha P. Kulkarni
Affiliation:
Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India, e-mail: [email protected]
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Abstract

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Over the last 20 years, since the publication of Sloan's paper on the improvement by the iteration technique, various approaches have been proposed for post-processing the Galerkin solution of multi-dimensional second kind Fredholm Integral equation. These methods include the iterated Galerkin method proposed by Sloan, the Kantorovich method and the iterated Kantorovich method. Recently, Lin, Zhang and Yan have proposed interpolation as an alternative to the iteration technique. For an integral operator, with a smooth kernel using the orthogonal projection onto a space of discontinuous piecewise polynomials of degree ≤ r − 1, previous authors have established an order r convergence for the Galerkin solution and 2r for the iterated Galerkin solution. Equivalent results have also been established for the interpolator projection at Gauss points and some interpolation post-processing technique. In this paper, a method is introduced and shown to have convergence of order 4r. The size of the system of equations that must be solved, in implementing this method, remains the same as for the Galerkin method.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 517 - 528
Copyright
Copyright © Australian Mathematical Society 2003

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