Higher order Galerkin–collocation time discretization with Nitsche’s method for the Navier–Stokes equations

We propose and study numerically the implicit approximation in time of Navier–Stokes equations by a Galerkin–collocation method combined with inf–sup stable finite element methods space. The conceptual basis approach is establishment direct connection between Galerkin classical collocation methods, perspective achieving accuracy former reduced computational costs terms less complex algebraic systems latter. Regularity higher order discrete solution ensured further. As an additional ingredient, we employ Nitsche’s to impose all boundary conditions weak form that evolving domains become feasible future. carefully compare performance properties standard continuous Galerkin–Petrov using piecewise linear polynomials time, algebraically equivalent popular Crank–Nicholson scheme. condition number arising after Newton linearization as well reliable drag lift coefficient for laminar flow around cylinder (DFG benchmark Re=100; cf. (Turek Schäfer, 1996)) are investigated. superiority over demonstrated therein.