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

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DOI: 10.4236/apm.2015.55024    3,578 Downloads   4,036 Views   Citations
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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