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Analysis of a three-field formulation of the Stokes problem. (Analyse d’une formulation à trois champs du problème de Stokes.) (French) Zbl 0791.76008
Summary: We study the numerical approximation of a three-fields formulation of Stokes problem. The unknowns are extra stress tensor, velocity and pressure. This formulation is motivated by the study of viscoelastic fluids obeying Oldroyd constitutive equation. We study the inf-sup conditions relating extra stress tensor, velocity and pressure. We give some examples of finite element spaces satisfying or not satisfying these conditions and we conclude by the study of a fixed point method to solve the approximate problem.

MSC:
76A10 Viscoelastic fluids
35Q30 Navier-Stokes equations
76M10 Finite element methods applied to problems in fluid mechanics
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