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IMA Journal of Numerical Analysis Advance Access originally published online on January 29, 2008
IMA Journal of Numerical Analysis 2008 28(3):619-646; doi:10.1093/imanum/drm043
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Uzawa-based adaptive methods for linear output functionals

Stefano Micheletti{dagger}, Simona Perotto{ddagger} and Marco Verani§

MOX—Politecnico di Milano, via Bonardi 9, I-20133 Milano, Italy

{dagger} Email: stefano.micheletti{at}polimi.it

{ddagger} Email: simona.perotto{at}polimi.it

§ Email: marco.verani{at}polimi.it

Received on 13 November 2005. Accepted for publication 31 January 2006.


  Abstract

In this paper, we address the approximation of a linear output functional J(u) to within a prescribed tolerance {tau}, u being the solution of an elliptic problem, via a new iterative procedure named adaptive goal-oriented (ago) algorithm. The core of this scheme is to extend to a goal-oriented setting the good properties of the adaptive Uzawa algorithm proposed in Dahlke et al. (2000, Math. Model. Numer. Anal., 34, 1003–1022), Dahlke et al. (2002, SIAM J. Numer. Anal., 40, 1230–1262) and Bänsch et al. (2002, SIAM J. Numer. Anal., 40, 1207–1229): reliability, automatism and flexibility in the choice of the discrete spaces. A convergence analysis of the ago algorithm is also carried out and some test cases are provided to assess its reliability in the 2D case.

Key Words: goal-oriented analysis; Uzawa algorithm; adaptive methods; elliptic partial differential equations


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