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

DOI: 10.4236/apm.2015.55024   PDF   HTML   XML   3,862 Downloads   4,425 Views   Citations

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.

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Zhou, S. and Hou, L. (2015) Least-Squares Finite Element Method for the Steady Upper-Convected Maxwell Fluid. Advances in Pure Mathematics, 5, 233-239. doi: 10.4236/apm.2015.55024.

Conflicts of Interest

The authors declare no conflicts of interest.

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