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Persistent URL http://purl.org/net/epubs/work/40512
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Record Id 40512
Title A stopping criterion for the conjugate gradient algorithm in a finite element method framework
Abstract The conjugate gradient method has always been successfully used in solving the symmetric and positive definite systems obtained by the finite element approximation of self-adjoint elliptic partial differential equations. Taking into account recent results by Golub and Meurant (1997), Meurant (1977), Meurant (1999a), and Strakos and Tichy (2003) which make it possible to approximate the energy norm of the error during the conjugate gradient iterative process, we adapt the stopping criterion introduced by Arioli, Noulard and Russo (2001). Moreover, we show that the use of the efficient preconditioners does not require to change the energy norm used by the stopping criterion. Finally, we present the results of several numerical tests that experimentally validate the effectiveness of our stopping criterion
Organisation CCLRC , CSE , CSE-NAG
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Language English (EN)
Type Details URI(s) Local file(s) Year
Journal Article Numerische Mathematik 97 (2004): 1-24. doi:10.1007/s00211-003-0500-y 2004
Report RAL Technical Reports RAL-TR-2002-034. 2002. RAL-TR-2002-034.pdf 2002