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

A least-squares mixed p-type finite element method is developed for numeric al solution of incompressible non-Newtonian flows. Hierarchical piecewise p olynomials are introduced as element basis functions while singularities an d boundary layers are treated by a combination of mesh redistribution and p olynomial refinement. Scaling of the original differential equations is fou nd to be important for the least-squares minimization process. We discuss b oth nonlinear algebraic and differential constitutive models and present nu merical examples to illustrate benefits and shortcomings of the present app roach. (C) 1999 Elsevier Science S.A. All rights reserved.