Journal of Scientific Computing

, Volume 27, Issue 1–3, pp 245–256

# Direct Minimization of the Discontinuous Least-Squares Spectral Element Method for Viscoelastic Fluids

Article

In this paper direct minimization of the discontinuous least-squares spectral element formulation is described. The method will beapplied to the Upper Convected Maxwell (UCM) model which describes a viscoelastic fluid. The new ideas presented in this paper consist of the weak coupling of the fluxes in the least-squares formulations instead of imposing weak continuity of the dependent variables. Furthermore, direct minimization is employed instead of the conventional variational least-squares formulation. The resulting system is solved iteratively using LSQR.

## Keywords

Viscoelastic flows spectral element method discontinuous least squares formulation direct minimization LSQR

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