Mixed finite element methods for viscoelastic flow analysis: A review

The progress made during the past decade in the application of mixed finite element methods to solve viscoelastic flow problems using differential constitutive equations is reviewed. The algorithmic developments are discussed in detail. Starting with the classical mixed formulation, the elastic viscous stress splitting (EVSS) method as well as the related discrete EVSS and the so-called EVSS-G method are discussed among others. Furthermore, stabilization techniques such as the streamline upwind PetrovGalerkin (SUPG) and the discontinuous Galerkin (DG) are reviewed. The performance of the numerical schemes for both smooth and non-smooth benchmark problems is discussed. Finally, the capabilities of viscoelastic flow solvers to predict experimental observations are reviewed.