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A three-field formulation for incompressible viscoelastic fluids. (English) Zbl 1231.76011

Summary: We present a new stabilized finite element method for incompressible viscoelastic fluids. A three-field formulation is developed wherein Oldroyd-B model is coupled with the mass and momentum conservation equations for an incompressible viscous fluid. The variational multiscale (VMS) framework is employed to develop a stabilized formulation for the coupled momentum, continuity and stress equations. Based on the new stabilized method a family of linear and higher-order triangle and quadrilateral elements with equal-order velocity-pressure-stress fields is developed. Stability and convergence property of the various elements is studied and optimal rates are attained in the norms considered. The method is applied to some benchmark problems and accuracy and computational economy of the formulation is investigated for various flow conditions.

MSC:

76A10 Viscoelastic fluids
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
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