Eigenvalue bounds for the Schur complement with a pressure convection-diffusion preconditioner in incompressible flow computations
When the stationary Navier-Stokes system is discretized in space by a mixed finite element method or an implicit time discretization of the corresponding evolution problem is linearized via a Picard iteration, a saddle point system arises which might be solved by Krylov subspace methods or by an Uzawa-type approach. For each of these methods it is necessary to precondition the Schur complement associated to the saddle point problem in question. Here the author finds upper and lower bounds on the eigenvalues of this Schur complement under the assumption that it is preconditioned by a pressure convection-diffusion matrix.
scientific article; zbMATH DE number 5559069