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

A fractional step θθ-method for the approximation of time-dependent viscoelastic fluid flow equations is described and analyzed in this article. The algorithm uses substeps within a time step to sequentially update velocity, pressure, and stress. This lagged approach to temporal integration requires a resolution of smaller systems than a fully implicit approach while achieving a second order temporal accuracy. We establish a priori error estimates for our scheme, and provide numerical computations to support the theoretical results and demonstrate the capability of this method.