Uzawa-based adaptive methods for linear output functionals

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