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Numerical analysis of the modified EVSS method. (English) Zbl 0896.76040
Summary: We present a proof of the stability of a new mixed finite element method introduced within the context of viscoelastic fluids. The mixed formulation is related to the EVSS (elastic-viscous-split-stress) method and is based on the rate of deformation tensor as an additional unknown. The proof applies to the Stokes flow and some linearized constitutive equations of slow viscoelastic flows. Existence and uniqueness of the continuous and the discrete problems are derived from a generalized Brezzi-Babuska theory. It is shown that no additional compatibility condition is required between the various variables except the usual one for the velocity and the pressure fields. This result allows to choose low order finite element for the stress. Several numerical experiments on the 4:1 contraction Stokes flow are presented which confirm the improved stability obtained with this new formulation.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76A10 Viscoelastic fluids
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