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

Shaoling Zhou^1,2*, Lei Hou¹

¹Department of Mathematics, Shanghai University, Shanghai, China.
²School of Science, Hebei University of Engineering, Handan, China.

DOI: 10.4236/apm.2015.55024                

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.

Keywords

Upper-Convected Maxwell Fluid, Least-Squares Finite Element Method, Viscoelastic Fluid Model

Conflicts of Interest

The authors declare no conflicts of interest.

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