A higher order fictitious domain method for the Navier–Stokes equations

We present a higher order approach for the numerical approximation of the Navier–Stokes equations of incompressible viscous flow on time‐dependent domains. A fictitious domain method using non body‐fitted finite element meshes for immersed and moving boundaries along with cut cell techniques is applied. Higher order discontinuous Galerkin time discretization schemes and inf‐sup stable pairs of finite elements for the discretization in space are further ingredients of the approach.