Dual-Mixed Finite Element Methods for Newtonian and Non-Newtonian Fluids
Jason Howell

Abstract: Accurate and efficient numerical methods to approximate fluid flows are important to researchers in many fields, including mechanical, materials, and biomedical engineering. In many applications within these fields, it is of paramount importance to accurately predict fluid stresses. However, most existing numerical schemes for fluids are formulated with velocity as the primary unknown of interest, and computation of the fluid stress requires expensive and potentially inaccurate postprocessing techniques. In this talk, a dual-mixed variational formulation for the Navier-Stokes equations, in which the stress is a primary unknown of interest, is derived and analyzed. Using results that provide equivalent sets of inf-sup conditions for twofold saddle point problems, it is shown that a finite element scheme for this method can be constructed from existing schemes for elasticity problems with weak symmetry of the stress. The extension of this method to non-Newtonian fluids is also discussed.