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International Journal of Computer Mathematics Volume 95, 2018 - Issue 1: Recent Trends in Highly Accurate and Structure-Preserving Numerical Methods for Partial Differential Equations
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Original Articles

Adaptive weights for mass conservation in a least-squares finite element method

Hsueh-Chen LeeGeneral Education Center, Wenzao Ursuline University of Languages, Kaohsiung, TaiwanCorrespondence[email protected]
[email protected]
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Pages 20-35 | Received 31 Oct 2016, Accepted 03 Oct 2017, Published online: 10 Nov 2017

References

  • J.H. Adler, T.A. Manteuffel, S.F. McCormick, J.W. Nolting, J.W. Ruge, and L. Tang, Efficiency based adaptive local refinement for first-order system least-squares formulations, SIAM J. Sci. Comput. 33 (2011), pp. 1–24. doi: 10.1137/100786897
  • P.B. Bochev and M.D. Gunzburger, Analysis of least-squares finite element methods for the Stokes equations, Math. Comput. 6 (1994), pp. 479–506. doi: 10.1090/S0025-5718-1994-1257573-4
  • P.B. Bochev and M.D. Gunzburger, Least-squares Finite Element Methods, Springer, New York, 2009.
  • P. Bolton and R.W. Thatcher, On mass conservation in least-squares methods, J. Comput. Phys. 203 (2005), pp. 287–304. doi: 10.1016/j.jcp.2004.08.013
  • Z. Cai, T.A. Manteufeel, and S.F. Mccormick, First-order system least-squares for velocity–vorticity–pressure form of the Stokes equations, with application to linear elastically, Electron. Trans. Numer. Anal. 3 (1995), pp. 150–159.
  • 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. doi: 10.1016/j.jnnfm.2009.02.004
  • C.L. Chang and J. Nelson, Least-squares finite element method for the Stokes problem with zero residual of mass conservation, SIAM J. Numer. Anal. 34 (1997), pp. 480–489. doi: 10.1137/S0097539794273368
  • C.L. Chang and S.Y. Yang, Analysis of the L2 least-squares finite element method for the velocity–vorticity–pressure Stokes equations with velocity boundary conditions, Appl. Math. Comput. 130 (2002), pp. 121–144.
  • J.M. Deang and M.D. Gunzburger, Issues related to least-squares finite element methods for the Stokes equations, SIAM J. Sci. Comput. 20 (1998), pp. 878–906. doi: 10.1137/S1064827595294526
  • J. Donea and A. Huerta, Finite Element Methods for Flow Problems, John Wiley and Sons Inc., Chichester, UK, 2003.
  • 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, Weighted least-squares finite element methods for the linearized Navier-Stokes equations, Int. J. Comput. Math. 91 (2014), pp. 1964–1985. doi: 10.1080/00207160.2013.864391
  • 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. 1993–1218. doi: 10.1137/130912682
  • 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. doi: 10.1016/j.jmaa.2015.07.012
  • H.C. Lee and T.F. Chen, A nonlinear weighted least-squares finite elements method for Stokes equations, Comput. Math. Appl. 59 (2010), pp. 215–224. doi: 10.1016/j.camwa.2009.08.033
  • J.L. Liu, Exact a posteriori error analysis of the least squares finite element method, Appl. Math. Comput. 116 (2000), pp. 297–305.
  • V. Prabhakar, J.P. Pontaza, and J.N. Reddy, A collocation penalty least-squares finite element formulation for incompressible flows, Comput. Methods Appl. Mech. Engrg. 197 (2008), pp. 449–463. doi: 10.1016/j.cma.2007.06.013
  • H.J. Yin, H. y. Zhong, and C.Q. Fu, Numerical simulations of viscoelastic flows through one slot channel, J. Hydrodyn. 19 (2007), pp. 201–216. doi: 10.1016/S1001-6058(07)60049-3

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