2014
DOI: 10.1016/j.apm.2014.04.049
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On the convergence of Variational multiscale methods based on Newton’s iteration for the incompressible flows

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Cited by 9 publications
(3 citation statements)
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“…Layton 2002;Kaya and Riviére 2005;John and Kaya 2005), this stabilization method is free of extra storage and easy to implement. It was subsequently applied to the unsteady Navier-Stokes equations (Shang 2013b) and combined with the two-grid methods (Li et al 2013;Shang and Qin 2016), the partition of unity method Xie and , and the adaptive technique (Zheng et al 2010;Shi et al 2014).…”
Section: Introductionmentioning
confidence: 99%
“…Layton 2002;Kaya and Riviére 2005;John and Kaya 2005), this stabilization method is free of extra storage and easy to implement. It was subsequently applied to the unsteady Navier-Stokes equations (Shang 2013b) and combined with the two-grid methods (Li et al 2013;Shang and Qin 2016), the partition of unity method Xie and , and the adaptive technique (Zheng et al 2010;Shi et al 2014).…”
Section: Introductionmentioning
confidence: 99%
“…Under the circumstance, it is necessary to define an appropriate operator, function spaces, and some additional dependent variables. Recently, a finite element VMS method based on two local Gauss integrations was proposed and developed by the authors of [21][22][23][24][25]. This finite element VMS method is simpler than the common finite element VMS method, 2 Mathematical Problems in Engineering which does not need additional dependent variables and the projection operator but keeps the same efficiency.…”
Section: Introductionmentioning
confidence: 99%
“…Implementation of VIM, has expanded because of the features of flexibility, handiness and accurateness, they possess. The implementations of the VIM methods are illustrated in [16][17][18][19][20]. This work, suggests that in various locations, Burger's equation can be solved precisely by the method of VIM.…”
Section: Introductionmentioning
confidence: 99%