TITLE:
Least-Squares Finite Element Method for the Steady Upper-Convected Maxwell Fluid
AUTHORS:
Shaoling Zhou, Lei Hou
KEYWORDS:
Upper-Convected Maxwell Fluid, Least-Squares Finite Element Method, Viscoelastic Fluid Model
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.5,
April
3,
2015
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 least-squares method to
the linearized version of the viscoelastic UCM model. The L2 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.