My research focuses on the efficient numerical solution of stationary partial differential equations arising in fluid dynamics. In particular, I study convection-diffusion equations and Stokes- and Oseen-type flow models, whose finite element discretization leads to large systems of linear equations. I investigate and compare the efficiency of various preconditioned iterative methods, including CGN, MINRES, GCR, GMRES, and Krylov–Uzawa methods, from both theoretical and numerical perspectives. Special attention is given to their convergence rates, dependence on different parameters, and possible stabilization techniques. My research also extends to the iterative solution of nonlinear fluid dynamics models. My main objective is to develop robust and rapidly convergent numerical methods that can be reliably applied under various flow conditions. The theoretical results are complemented by computer implementations and numerical experiments.