Abstract
In this paper, a fully discrete fractional semi-implicit FEM-scheme is developed to study the non-Newtonian fluid flow of polymer aqueous solutions in a two-dimensional domain using Caputo's fractional time-derivative. The fractional-time scheme is coupled with the spatial discretization using the Galerkin finite element method. The existence and uniqueness results were obtained for the weak discrete solution and with the help of a newly introduced trilinear form. The convergence and stability of the elaborated numerical scheme are demonstrated for certain criteria and temporal step bounds are obtained. Numerical simulations are elaborated and the effects of various parameters of the discrete system are investigated. The obtained results are analyzed and application to the lid-driven cavity problem in complex geometry is presented.