The stabilized penalty-projection finite element method for the Navier-Stokes-Cahn-Hilliard-Oono system
type: Item
instance of: scholarly article
title: The stabilized penalty-projection finite element method for the Navier-Stokes-Cahn-Hilliard-Oono system
zbMATH Open document ID: 1468.76043
author: Xue Wang
author: Bo Wang
author: Guang-an Zou
published in: Applied Numerical Mathematics
publication date: 2021-06-03T00:00:00Z
review text: The authors are concerned with the penalty-projection FEM as a solver for the Navier-Stokes-Cahn-Hilliard-Oono system in a bounded 2D domain modeling the phase-field of two-phase flows. They introduce a mixed finite element method to solve the penalized system instead of the original one and derive the optimal error estimates for finite element approximation in the case of piecewise linear basis functions. Then, they consider two stabilized fully discrete schemes for the original formulation, based on time discretization of the penalized finite element system. The backward-Euler scheme and the penalty-projection scheme are proposed for the temporal approximation. The convergence of both fully discrete schemes is proved. These discrete schemes remain stable and satisfy energy laws. Some numerical experiments are carried out in order to prove the validity and effectiveness of the proposed scheme, and to simulate the phenomena of thrombus motion in atherosclerosis flow.
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76T99
Mathematics Subject Classification ID: 76Z05
Mathematics Subject Classification ID: 92C35
zbMATH DE Number: 7354396
zbMATH Keywords: phase-field two-phase flow model
zbMATH Keywords: stabilized penalty-projection scheme
zbMATH Keywords: mixed finite element discretization
zbMATH Keywords: backward-Euler scheme
zbMATH Keywords: optimal error estimate
zbMATH Keywords: atherosclerosis flow
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: j.apnum.2021.03.004
OpenAlex ID: W3134165987
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DOI: 10.1016/J.APNUM.2021.03.004
description: scientific article; zbMATH DE number 7354396