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. •The application of the Isogeometric Finite Cell Method to mixed formulations is studied.•The performance of four families of isogeometric mixed finite elements is compared.•For all considered elements the inf–sup stability is tested using a generic Stokes test case.•A detailed mesh convergence study is performed to assess the optimality of all elements.