# Meeting Details

Title: Cascadic Multilevel Algorithms for Saddle Point Systems CCMA PDEs and Numerical Methods Seminar Series Constantin Bacuta, Department of Mathematical Sciences , University of Delaware Based on the cascade principle, we consider multilevel type of algorithms for discretizing saddle point problems. The finite element spaces are associated with successively finer and finer grids. On each fixed level a standard Uzawa, gradient Uzawa, or conjugate gradient Uzawa method is implemented. The algorithms are designed to perform more iterations on the coarse grids and fewer on the fine grids. The level change criteria is based on keeping the iteration error close to expected discretization error. To decrease the running time, the iteration on each new level starts with the best approximation from the previous level. Numerical results supporting the efficiency of the algorithms are presented for the Stokes system. We use our general theory to introduce/review the saddle point least-squares'' method and relate it with the Bramble-Pasciak's least square approach. As a consequence, we design a least-squares iterative solver for the time harmonic Maxwell equations. This is joint work with Francisco Sayas, and Lu Shu.