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Cited by 95 publications
(106 citation statements)
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“…The convergence of this scheme on any fixed time interval can be derived via standard methods (see for instance [34]). …”
Section: 4)mentioning
confidence: 99%
See 1 more Smart Citation
“…The convergence of this scheme on any fixed time interval can be derived via standard methods (see for instance [34]). …”
Section: 4)mentioning
confidence: 99%
“…The new alternative treatment of the nonlinear advection term proves to be crucial in our long time stability analaysis. There is a long list of work on time and spatial discretization of the NSE and related dissipative systems that preserves the dissipativity in various forms (see for instance [10,11,15,22,23,24,25,29,34,37,38,46,55] among many others). In particular, a general framework for the convergence of global attractor (in upper semicontinous fashion) for one step scheme was derived by Hale, Lin and Raugel [21].…”
Section: 4)mentioning
confidence: 99%
“…u comes from the term (u · ∇)u in the PDE (1). According to [3], [4] in case of stationarity and a su ciently smooth right hand side there exists at most one strong solution for the velocity u, whereas the solution for the pressure is only de ned up to an additive constant [5].…”
Section: Dirichlet Conditionmentioning
confidence: 99%
“…[19]). Taking the divergence of (3.3a) and using (3.3b) to eliminate the unknown velocity u n+1 yields a non-linear elliptic problem for the pressure.…”
Section: A Fractional Step Algorithm For Dispersed Two-phase Flowsmentioning
confidence: 99%
“…To this purpose, we use a fractional step algorithm of the class of finite element projection methods, which are widely used for incompressible flows, see e.g. [17,19] and references herein. An extension to the barotropic NavierStokes equations close to the scheme developed here can be found in [14], together with references to related works.…”
Section: Introductionmentioning
confidence: 99%