article

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

Authors:

J. H. Carneiro de Araujo,

V. RuasAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 234, Issue 8

Pages 2562 - 2577

https://doi.org/10.1016/j.cam.2010.03.025

Published: 01 August 2010 Publication History

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.

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Cited By

Leal Toledo RRuas V(2011)Numerical analysis of a least-squares finite element method for the time-dependent advection-diffusion equationJournal of Computational and Applied Mathematics10.1016/j.cam.2011.02.022235:12(3615-3631)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1016/j.cam.2011.02.022

Study of a finite element method for the time-dependent generalized Stokes system associated with viscoelastic flow
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
    2. Numerical analysis
2. Theory of computation

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cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 234, Issue 8

August, 2010

250 pages

ISSN:0377-0427

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Copyright © Elsevier B.V. © 2010.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 August 2010

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Cited By

Leal Toledo RRuas V(2011)Numerical analysis of a least-squares finite element method for the time-dependent advection-diffusion equationJournal of Computational and Applied Mathematics10.1016/j.cam.2011.02.022235:12(3615-3631)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1016/j.cam.2011.02.022

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