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International Journal of Computer Mathematics Volume 98, 2021 - Issue 10
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Research Article

An adaptive least-squares finite element method for Giesekus viscoelastic flow problems

Hsueh-Chen Leea General Education Center, Wenzao Ursuline University of Languages, Kaohsiung, TaiwanCorrespondence[email protected]
&
Hyesuk Leeb School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, USA
Pages 1974-1990 | Received 19 Jul 2020, Accepted 03 Dec 2020, Published online: 18 Jan 2021

References

  • M.A. Alves, P.J. Oliveira, and F.T. Pinho, Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions, J. Non-Newton. Fluid Mech. 110 (2003), pp. 45–75.
  • R.B. Bird, R.C. Armstrong, and O. Hassager, Fluid Mechanics, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics, 2nd ed., John Wiley and Sons, New York, 1987.
  • Z. Cai and C.R. Westphal, An adaptive mixed least-squares finite element method for viscoelastic fluids of Oldroyd type, J. Non-Newton. Fluid Mech. 159 (2009), pp. 72–80.
  • O.M. Coronado, D. Arora, M. Behr, and M. Pasquali, Four-field Galerkin/least-squares formulation for viscoelastic fluids, J. Non-Newton. Fluid Mech. 140 (2006), pp. 132–144.
  • T.F. Chen, C.L. Cox, H.C. Lee, and K.L. Tung, Least-squares finite element methods for generalized Newtonian and viscoelastic flows, Appl. Numer. Math. 60 (2010), pp. 1024–1040.
  • J.H. Chaudhry, S.D. Bond, and L.N. Olson, A weighted adaptive least-squares finite element method for the Poisson-Boltzmann equation, Appl. Math. Comput. 218 (2012), pp. 4892–4902.
  • H. Giesekus, A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tonsorial mobility, J. Non-Newton. Fluid Mech. 11 (1982), pp. 69–109.
  • R. Keunings, On the high Weissenberg number problem, J. Non-Newton. Fluid Mech. 20 (1986), pp. 209–226.
  • H.C. Lee, A nonlinear weighted least-squares finite element method for the Oldroyd-B viscoelastic flow, Appl. Math. Comput. 219 (2012), pp. 421–434.
  • H.C. Lee and H. Lee, Numerical simulations of viscoelastic fluid flows past a transverse slot using least-squares finite element methods, J. Sci. Comput. 79 (2019), pp. 369–388.
  • J.L. Liu, Exact a posteriori error analysis of the least squares finite element method, Appl. Math. Comput. 116 (2000), pp. 297–305.
  • H.C. Lee, An adaptively refined least-squares finite element method for generalized Newtonian fluid flows using the Carreau model, SIAM J. Sci. Comput. 36 (2014), pp. 193–218.
  • H.C. Lee and T.F. Chen, Adaptive least-squares finite element approximations to Stokes equations, J. Comput. Appl. Math. 280 (2015), pp. 396–424.
  • H.C. Lee, A nonlinear weighted least-squares finite element method for the Carreau-Yasuda non-Newtonian model, J. Math. Anal. Appl. 432 (2015), pp. 844–861.
  • H.C. Lee, Adaptive weights for mass conservation in a least-squares finite element method, Int. J. Comput. Math. 95 (2018), pp. 20–35.
  • M.T. Ravanchi, M. Mirzazadeh, and F. Rashidi, Flow of Giesekus viscoelastic fluid in a concentric annulus with inner cylinder rotation, Int. J. Heat Fluid Flow 28 (2007), pp. 838–845.
  • N. Thongjub, B. Puangkird, and V. Ngamaramvaranggul, Slip effect study of 4:1 contraction flow for Oldroyd-B model, Int. J. Math., Comput. Phys., Elect. Comput. Eng. 7 (2013), pp. 1334–1341.
  • S. Zhou and L. Hou, A weighted least-squares finite element method for Phan-Thien-Tanner viscoelastic fluid, J. Math. Anal. Appl. 436 (2016), pp. 66–78.

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