An optimal three-field finite element approximation of the Stokes system with continuous extra stresses. (English) Zbl 0797.76045

Summary: The aim is to present a mixed finite element method for solving the two- dimensional Stokes system, written in terms of the variables velocity, pressure and extra stress tensor. A convenient functional framework is introduced, allowing simpler choices of the type of approximation for the third variable. This is assumed here to be continuous, in order to ensure its applicability to viscoelastic flow problems. In the particular second order Galerkin method that is studied, the dimension of the corresponding finite element subspace is reduced to a minimum, at least as far as local stability analyses are concerned.


76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
76A10 Viscoelastic fluids
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