Learn More
We describe an effective solver for the discrete Oseen problem based on an augmented Lagrangian formulation of the corresponding saddle point system. The proposed method is a block triangular preconditioner used with a Krylov subspace iteration like BiCGStab. The crucial ingredient is a novel multigrid approach for the (1,1) block, which extends a technique(More)
SUMMARY We study different variants of the augmented Lagrangian-based block triangular preconditioner introduced by the first two authors in [SIAM J. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual (GMRES) method applied to various finite element and MAC discretizations of the Oseen problem in two and three(More)
Incompressible unsteady Navier–Stokes equations in pressure – velocity variables are considered. By use of the implicit and semi-implicit schemes presented the resulting system of linear equations can be solved by a robust and efficient iterative method. This iterative solver is constructed for the system of linearized Navier–Stokes equations. The Schur(More)
We consider several preconditioners for the pressure Schur complement of the discrete steady Oseen problem. Two of the preconditioners are well known from the literature and the other is new. Supplemented with an appropriate approximate solve for an auxiliary velocity subproblem these approaches give rise to a family of the block preconditioners for the(More)
In this note we consider discrete linear reaction-diffusion problems. For the discretization a standard conforming finite element method is used. For the approximate solution of the resulting discrete problem a multigrid method with a damped Jacobi or symmetric Gauss-Seidel smoother is applied. We analyze the convergence of the multigrid V- and W-cycle in(More)
We consider an abstract parameter dependent saddle-point problem and present a general framework for analyzing robust Schur complement preconditioners. The abstract analysis is applied to a generalized Stokes problem , which yields robustness of the Cahouet-Chabard preconditioner. Motivated by models for two-phase incompressible flows we consider a(More)
The paper concerns with an iterative technique for solving discretized Stokes type equations with varying viscosity coefficient. We build a special block preconditioner for the discrete system of equations and perform an analysis revealing its properties. The subject of this paper is motivated by numerical solution of incompressible non-Newtonian fluid(More)
In this paper, we study numerical methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in R d defines a d-dimensional space-time manifold in the space-time continuum R d+1. We derive and analyze a variational formulation for a class of diffusion problems on the space-time manifold. For this variational(More)