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Piecewise linear finite element approximation of a generalized Stokes system related to viscolelastic flow. (English) Zbl 1432.76167

Summary: A three-field finite element scheme designed for solving systems of partial differential equations governing stationary viscoelastic flows is studied. It is based on the simulation of a time-dependent behavior. Once a classical time-discretization is performed, the resulting three-field system of equations allows for a stable approximation of velocity, pressure and extra stress tensor, by means of continuous piecewise linear finite elements, in both two and three dimension space. This is proved to hold for the linearized form of the system. An advantage of the new formulation is the fact that it implicitly provides an algorithm for the iterative resolution of system non-linearities. Convergence in an appropriate sense applying to these three flow fields is demonstrated.

MSC:

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