Finite element approximation of kinetic dilute polymer models with microscopic cut-off (Q2836468)

This interesting paper is concerned with a FEM for the weak solutions to the incompressible Navier-Stokes equations in a bounded domain of \(\mathbb{R}^d, \;d=2,3\), with an elastic extra-stress tensor in the momentum equation, which is a model arising from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The extra-stress tensor stems from the random movement of the polymer chains, being defined through the associated probability density function that satisfies a Fokker-Planck type parabolic equation. The convergence (on a subsequence) of this FEM is proved under suitable conditions on the data (as the spatial and temporal discretization parameters tend to \(0\)), thus showing the existence of a weak solution to the corresponding Navier-Stokes-Fokker-Planck system.