Nonlinear uzawa methods for solving nonsymmetric saddle point problems

Block triangular Schur complement preconditioners for saddle point problems and application to the Oseen equations

“…One is a finite element subdivision based on ne × ne uniform grids of square elements, the mixed finite element used is the bilinear-constant velocity-pressure ( Q 1 − P 0 ) element [27] with global stabilization or local stabilization (cf. [4,[26][27][28]). The second is a "marker and cell" (MAC) finite difference scheme (cf.…”

“…For some problems, especially those arising in constrained optimization and in mixed finite element discretization of the linearized Navier-Stokes equations [1,9], C = B and D = 0. For others, such as those arising from stabilized finite elements [4,9,21,[26][27][28], C = B, D = 0 but D is small. In addition, if one uses spectral (Chebyshev collocation) approach to discretize, for example, the Stokes equations, then one has a (generalized) saddle point system with C = B was considered by Murphy et al [19].…”

The Preconditioner of GPHSS Method for Saddle Point Systems

“…For the saddle point problem (augmented system) (m > n) is of full column rank, m R p ∈ and n R q ∈ , there are many kinds of iterative methods such as Uzawa [3], SOR-like [4], GSI [6], GAOR [8], HSS [1] and PHSS [2]. Based on the PHSS method, Pan and Wang [7] suggested a GPHSS method with two parameters.…”

On generalized stationary iterative method for solving the saddle point problems

“…For its property of large and sparsity, system (1.1) is suitable for being solved by the iterative methods. There are many efficient iterative methods have been studied in the literature, see [2][3][4][5][6][7][8][9][10]. Recently, Golub et al [2] proposed the SOR-like method and considered the optimum choice for iterative parameter.…”