Reduced basis approximation and a posteriori error estimates for a multiscale liquid crystal model

We present a reduced basis framework and associated a posteriori error estimates for the multiscale Stokes Fokker-Planck system that governs the flow of a dilute suspension of rod-like molecules immersed in a Newtonian solvent, relevant in liquid crystals modelling. The Fokker-Planck equation dictates the microscale behaviour and must be solved at every quadrature point of the macroscale finite element mesh - this is a natural example of a many-query problem for which the certified reduced basis method is well suited. We focus on a Poiseuille flow problem to simplify the presentation of ideas, but we note that the methods developed in this article generalize directly to more complicated problems. Numerical results demonstrate that our reduced basis approach leads to significant computational savings and also that our error estimator performs well for moderate parameter values.