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In this paper we propose a new class of preconditioners for the isogeometricdiscretization of the Stokes system. Their application involves the solution ofa Sylvester-like equation, which can be done efficiently thanks to the FastDiagonalization method. These preconditioners are robust with respect to boththe spline degree and mesh size. By incorporating information on the geometryparametrization and equation coefficients, we maintain efficiency onnon-trivial computational domains and for variable kinematic viscosity. In ournumerical tests we compare to a standard approach, showing that the overalliterative solver based on our preconditioners is significantly faster.

Robust isogeometric preconditioners for the Stokes system based on the Fast Diagonalization method