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Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model

Abstract : In this paper, we construct a fully discrete numerical scheme for approximating a two-dimensional multiphasic incompressible fluid model, also called the Kazhikhov-Smagulov model. We use a first-order time discretization and a splitting in time to allow us the construction of an hybrid scheme which combines a Finite Volume and a Finite Element method. Consequently, at each time step, one only needs to solve two decoupled problems, the first one for the density and the second one for the velocity and pressure. We will prove the stability of the scheme and the convergence towards the global in time weak solution of the model.
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Submitted on : Tuesday, September 12, 2017 - 3:41:21 PM
Last modification on : Friday, July 8, 2022 - 10:09:17 AM
Long-term archiving on: : Wednesday, December 13, 2017 - 3:17:13 PM

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Caterina Calgaro, Meriem Ezzoug, Ezzeddine Zahrouni. Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model. Communications on Pure and Applied Analysis, AIMS American Institute of Mathematical Sciences, 2018, 17 (2), pp.429-448. ⟨10.3934/cpaa.2018024⟩. ⟨hal-01586201⟩

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