Iterative solvers for quadratic discretizations of the generalized Stokes problem

摘要

We present in this paper various iterative methods for the solution of large linear and non-linear systems resulting from the discretization of the generalized Stokes problem. A second-order (O(h~2)) P_2-P_1 mixed finite element is used for the approximation of the velocity and the pressure. Solution strategies based on conjugate gradient-like methods, the Uzawa's and Arrow-Hurwicz's methods are presented. Schur complement methods are also explored in the context of a hierarchical decomposition of the velocity field. The ever present preconditioning problem is also addressed. The performance of these iterative methods will be discussed on complex flows of industrial interest.