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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

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Volume 18, Issue 2

Issues

Semi-Discrete Galerkin Finite Element Method for the Diffusive Peterlin Viscoelastic Model

Yao-Lin Jiang
  • Corresponding author
  • School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P. R. China
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/ Yun-Bo Yang
Published Online: 2017-07-06 | DOI: https://doi.org/10.1515/cmam-2017-0021

Abstract

In this paper, a semi-discrete Galerkin finite element method is applied to the two-dimensional diffusive Peterlin viscoelastic model which can describe the unsteady behavior of some incompressible ploymeric fluids. For the derived semi-discrete finite element spatial discretization scheme, the a priori bounds are given that does not rely on the mesh width restriction. Further, with the help of the a priori error bounds of the Stokes and Ritz projections, optimal error estimates for the velocity, the conformation tensor and the pressure are presented, respectively. Finally, in order to implement the proposed semi-discrete numerical scheme, we derive three kinds of fully discrete schemes, e.g., Newton’s iterative scheme, Picard’s iterative scheme and implicit-explicit time-stepping scheme. Finally, several numerical experiments are conducted to confirm our theoretical results.

Keywords: Peterlin Viscoelastic Model; Semi-Discrete Scheme; Finite Element Method; Error Estimate

MSC 2010: 65N15; 65N30; 65N12; 65M12

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About the article

Received: 2016-12-19

Revised: 2017-06-02

Accepted: 2017-06-19

Published Online: 2017-07-06

Published in Print: 2018-04-01


Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11371287

Award identifier / Grant number: 61663043

This work was supported by the Natural Science Foundation of China (11371287, 61663043) and the Natural Science Basic Research Plan in Shaanxi Province of China (2016JM5077).


Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 2, Pages 275–296, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2017-0021.

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