An Adaptive Uzawa Algorithm for Output Functionals Control
Tuesday 3rd May 2005
Micheletti, Stefano; Perotto, Simona; Verani, Marco
In this paper we address the approximation of a linear output functional J(u), where u is the solution of an elliptic problem, through suitable duality arguments. In particular, moving from the adaptive Uzawa algorithm proposed by E. Baensch et al. and S. Dahlke et al., we first cast the original problem in a saddle-point formulation and then we provide two new algorithms for computing an approximation $u_h$ to $u,$ such that $|J(u) - (u_h)|$ be below a prescribed tolerance t. Some test cases are included to assess the reliability of the proposed method in the 1D case togheter with some preliminary two dimensional results.