If the Navier-Stokes equations for incompressible fluids are linearized using fixed point iterations, the Oseen equations arise. In this thesis we provide concepts for the coupled algebraic multigrid (AMG) solution of this saddle point system, where coupled here is meant in contrast to methods, where pressure and velocity equations are iteratively decoupled, and 'standard' AMG is used for the solution of the resulting scalar problems.

We show how the coarse levels can be constructed (where their stability is an important issue) and which smoothers (known from geometric multigrid methods for saddle point systems) can be used.

To prove the efficiency of our methods experimentally, we apply them to finite element discretizations of various problems (model problems and also more complex industrial settings) and compare them with classical approaches.

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