Adaptive wavelet methods for saddle point problems

Recently, adaptive wavelet stratégies for symmetrie, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetrie, but indefinite. Firstly, we investigate a posteriori error estimâtes and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator. As an alternative, we introducé an adaptive variant of Uzawa's algorithm and prove its convergence. Secondly, we dérive explicit criteria for adaptively refined wavelet spaces in order to fulfill the LadyshenskajaBabuska-Brezzi (LBB) condition and to be fully equilibrated. Mathematics Subject Classification. 65J10, 65T60, 42C40. Received: April 16, 1999. Revised: March 31, 2000.