Adaptive geometric multigrid for the mixed finite cell formulation of Stokes and Navier–Stokes equations

The unfitted finite element methods have emerged as a popular alternative to classical for the solution of partial differential equations and allow modeling arbitrary geometries without need boundary-conforming mesh. On other hand, efficient resultant system is challenging task because numerical ill-conditioning that typically entails from formulation such methods. We use an adaptive geometric multigrid solver mixed cell saddle-point problems investigate its convergence in context Stokes Navier–Stokes equations. present two smoothers treatment cutcells method analyze their effectiveness model using benchmark. Results indicate presented capable solving independently problem size robust with respect depth grid hierarchy.