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Finite element approximation of viscoelastic progressively incompressible flows. (English) Zbl 0681.76010
Summary: To avoid any numerical locking in the finite element approximation of viscoelastic flow problems, we propose a three-field approximation of this problem. This approximation, which involves velocities, stresses, and pressures is proved to converge for all times. In the proof, we also obtain convergence results for the three-fields finite element approximation of incompressible elasticity problems.

MSC:
76A05 Non-Newtonian fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
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