Finite elements for viscoelastic flows with change of type

The authors compare several mixed finite-element methods for calculating viscoelastic flows where the vorticity equation changes type from elliptic to hyperbolic whenever inertia is taken into account. The flows are perturbed viscometric flows with slightly wavy walls. The perturbed uniform flow gives rise to a closed-form analytical solution. They examine five different finite-element algorithms; it is found that the so-called SU4*4 and EVSS methods perform much better than the other three. They also examine a number of features proper to flows with change of type, such as the propagation of disturbances along characteristic lines of the vorticity equation.