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

Caterina Calgaro; Meriem Ezzoug; Ezzeddine Zahrouni

doi:10.3934/cpaa.2018024

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2018, Volume 17, Issue 2: 429-448. Doi: 10.3934/cpaa.2018024

This issue Previous Article The regularity of some vector-valued variational inequalities with gradient constraints Next Article On the effect of higher order derivatives of initial data on the blow-up set for a semilinear heat equation

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

1.
Univ. Lille, CNRS, UMR 8524 -Laboratoire Paul Painlevé, F-59000 Lille, France
2.
Unité de recherche : Multifractals et Ondelettes, FSM, University of Monastir, 5019 Monastir, Tunisia
3.
FSEGN, University of Carthage, 8000 Nabeul, Tunisia

* Corresponding author
* Corresponding author

Received: May 31, 2016

Revised: August 31, 2017

Published: June 2018

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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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Mathematics Subject Classification: Primary:35Q35, 65M12, 65M60, 65M08;Secondary:35B50.

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