Mixed Isogeometric Finite Cell Methods for the Stokes problem

We study the application of the Isogeometric Finite Cell Method (IGA-FCM) to mixed formulations in the context of the Stokes problem. We investigate the performance of the IGA-FCM when utilizing some isogeometric mixed finite elements, namely: Taylor–Hood, Sub-grid, Raviart–Thomas, and Nédélec elements. These element families have been demonstrated to perform well in the case of conforming meshes, but their applicability in the cut-cell context is still unclear. Dirichlet boundary conditions are imposed by Nitsche's method. Numerical test problems are performed, with a detailed study of the discrete inf–sup stability constants and of the convergence behavior under uniform mesh refinement.