Study of a finite element method for the time-dependent generalized Stokes system associated with viscoelastic flow

Authors:
J. H. Carneiro de Araujo;P. D. Gomes;V. Ruas
Affiliations:
Departamento de Ciência da Computação, Universidade Federal Fluminense, Niterói, Rio de Janeiro state, Brazil and Programa de Pós-Graduação em Ciência da Co ...;Programa de Pós-Graduação em Ciência da Computação, Universidade Federal Fluminense, Niterói, Rio de Janeiro state, Brazil;Programa de Pós-Graduação em Ciência da Computação, Universidade Federal Fluminense, Niterói, Rio de Janeiro state, Brazil and UPMC Univ. Paris 6, UMR 7190, Inst ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 6
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Abstract

A three-field finite element scheme designed for solving systems of partial differential equations governing time-dependent viscoelastic flows is studied. Once a classical backward Euler 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- dimensional space. This is proved to hold for the linearized form of the system. An advantage of the new formulation is the fact that it provides an algorithm for the explicit iterative resolution of system nonlinearities. Convergence in an appropriate sense applying to these three flow fields is demonstrated.