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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