The efficiency of a nudging data assimilation algorithm using higher order finite element interpolating operators is studied. Numerical experiments are presented for the 2D Navier–Stokes equations in three cases: shear flow an annulus, forced disk with off-center cavity, and box all satisfying Dirichlet boundary conditions. In cases, second interpolation coarse-grain shown to outperform first i...

In this paper, we introduce a new Virtual Element Method (VEM) not requiring any stabilization term based on the usual enhanced first-order VEM space. The method relies modified formulation of discrete diffusion operator that ensures stability preserving all properties differential operator.