A fractional step θ-method approximation of time-dependent viscoelastic fluid flow

A fractional step θ-method for the approximation of time dependent viscoelastic fluid flow equations, is described and analyzed in this article. The θ-method implementation allows the velocity and pressure updates to be resolved separately from the stress, reducing the number of unknowns resolved at each step of the method. A streamline upwinded Petrov-Galerkin (SUPG)-method is used to stabilize the constitutive equation. A priori error estimates are established for the approximation scheme. Numerical computations supporting the theoretical results and demonstrating the θ-method are also presented.