Abstract
In this paper, we address the approximation of a linear output functional J(u) to within a prescribed tolerance τ, 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 Bansch 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.
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