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Spectral refinement using a new projection method

DSpace at IIT Bombay

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Title Spectral refinement using a new projection method
 
Creator KULKARNI, RR
GNANESHWAR, N
 
Subject galerkin approximations
superconvergence
eigenvalue
equations
 
Description In this paper we consider two spectral refinement schemes, elementary and double iteration, for the approximation of eigenelements of a compact operator using a new approximating operator. We show that the new method performs better than the Galerkin, projection and Sloan methods. We obtain precise orders of convergence for the approximation of eigenelements of an integral operator with a smooth kernel using either the orthogonal projection onto a spline space or the interpolatory projection at Gauss points onto a discontinuous piecewise polynomial space. We show that in the double iteration scheme the error for the eigenvalue iterates using the new method is of the order of h(4r)(h(3r))(k), where h is the mesh of the partition and k = 0, 1, 2,... denotes the step of the iteration. This order of convergence is to be compared with the orders h(2r)(h(r))k in the Galerkin and projection methods and h(2r)(h(2r))(k) in the Sloan method. The error in eigenvector iterates is shown to be of the order of h(3r)(h(3r))(k) in the new method, h(r)(h(r))(k) in the Galerkin and projection methods and h(2r)(h(2r))(k) in the Sloan method. Similar improvement is observed in the case of the elementary iteration. We show that these orders of convergence are preserved in the corresponding discrete methods obtained by replacing the integration by a numerical quadrature formula. We illustrate this improvement in the order of convergence by numerical examples.
 
Publisher AUSTRALIAN MATHEMATICS PUBL ASSOC INC
 
Date 2011-07-18T21:45:12Z
2011-12-26T12:50:51Z
2011-12-27T05:36:59Z
2011-07-18T21:45:12Z
2011-12-26T12:50:51Z
2011-12-27T05:36:59Z
2004
 
Type Article
 
Identifier ANZIAM JOURNAL, 46(), 203-224
1446-1811
http://dspace.library.iitb.ac.in/xmlui/handle/10054/5081
http://hdl.handle.net/10054/5081
 
Language en