The finite element solution of a quasi-linear elliptic equation governing non-Newtonian flows through rectangular ducts

A Rayleigh-Ritz finite element method (FEM) using quadratic, cubic and quartic elements has been used to solve the steady laminar flow of a non-Newtonian fluid through rectangular ducts. Different iterative approaches were investigated to solve the large system of linear equations resulting from the discretization of the quasi-linear partial differential equation. The performance of the FEM incorporating the method of variation of parameters (Davidenko path procedure) was compared with the finite difference method in terms of speed, accuracy and the capability of handling the very pronounced nonlinearity. From the convergent solutions obtained, some flow parameters were investigated. The results presented agree well with other published work.