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A superconvergence result for solutions of compact operator equations

DSpace at IIT Bombay

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Title A superconvergence result for solutions of compact operator equations
 
Creator KULKARNI, RP
 
Subject 2nd kind
integral-equations
galerkin approximations
collocation
 
Description Over the last 20 years, since the publication of Sloan's paper on the improvement by the iteration technique, vaxious 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 less than or equal to 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 interpolatory 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.
 
Publisher AUSTRALIAN MATHEMATICS PUBL ASSOC INC
 
Date 2011-07-18T21:22:43Z
2011-12-26T12:50:50Z
2011-12-27T05:36:58Z
2011-07-18T21:22:43Z
2011-12-26T12:50:50Z
2011-12-27T05:36:58Z
2003
 
Type Article
 
Identifier BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 68(3), 517-528
0004-9727
http://dspace.library.iitb.ac.in/xmlui/handle/10054/5074
http://hdl.handle.net/10054/5074
 
Language en