An all‐at‐once algebraic multigrid method for finite element discretizations of Stokes problem

We consider numerical solution of finite element discretizations the Stokes problem. focus on transform-then-solve approach, which amounts to first apply a specific algebraic transformation linear system equations arising from discretization, and then solve transformed with an multigrid method. The approach has recently been applied difference problem constant viscosity, recommended itself as robust competitive In this work, we examine extension standard problem, including problems variable viscosity. relies, one hand, use successive over-relaxation method smoother for some schemes. On other present strategies that allow us limit complexity increase induced by transformation. Numerical experiments show stationary our is compared reference solver based block diagonal preconditioner MINRES, suggest also more robust. particular, demonstrates significant speed-up respect preconditioner. particularly time-dependent whatever time step size.