Least-Squares Finite Element Method for the Steady Upper-Convected Maxwell Fluid

Abstract

In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a leastsquares method to the linearized version of the viscoelastic UCM model. The L 2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.