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.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11371287
Award Identifier / Grant number: 61663043
Funding statement: 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).
Acknowledgements
The authors would like to thank the editor and anonymous referees for their careful reading and valuable comments, which led to great improvement of the present article.
References
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