Least-squares p-r finite element methods for incompressible non-Newtonian flows

A least-squares mixed p-type finite element method is developed for numerical solution of incompressible non-Newtonian flows. Hierarchical piecewise polynomials are introduced as element basis functions while singularities and boundary layers are treated by a combination of mesh redistribution and polynomial refinement. Scaling of the original differential equations is found to be important for the least-squares minimization process. We discuss both nonlinear algebraic and differential constitutive models and present numerical examples to illustrate benefits and shortcomings of the present approach.