Piecewise Linear Finite Element Approximation of a Generalized Stokes System Related to Viscolelastic Flow

V. Ruas, A.P. Brasil, J.H. Carneiro de Araujo
Received 14 December, 2010; accepted in revised form 25 April, 2012
Abstract: A three-field finite element scheme designed for solving systems of partial dif-
ferential 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 algo-
rithm for the iterative resolution of system non-linearities. Convergence in an appropriate
sense applying to these three flow fields is demonstrated.


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