Cai, Z. and Westphal, C.R. (2009) An Adaptive Mixed Least-Squares Finite Element Method for Viscoelastic Fluids of Oldroyd Type. Journal of Non-Newtonian Fluid Mechanics, 159, 72-80.
http://dx.doi.org/10.1016/j.jnnfm.2009.02.004

has been cited by the following article:

• 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.