Finite volume methods: foundation and analysis

T Barth, R Herbin, M Ohlberger - … of computational mechanics …, 2018 - Wiley Online Library
Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlap** control volumes. Degrees of …

Keller-Segel chemotaxis models: A review

G Arumugam, J Tyagi - Acta Applicandae Mathematicae, 2021 - Springer
We recount and discuss some of the most important methods and blow-up criteria for
analyzing solutions of Keller-Segel chemotaxis models. First, we discuss the results …

[HTML][HTML] A nonlinear time compactness result and applications to discretization of degenerate parabolic–elliptic PDEs

B Andreianov, C Cancès, A Moussa - Journal of Functional Analysis, 2017 - Elsevier
We propose a discrete functional analysis result suitable for proving compactness in the
framework of fully discrete approximations of strongly degenerate parabolic problems. It is …

An unconditionally energy stable and positive upwind DG scheme for the Keller–Segel model

D Acosta-Soba, F Guillén-González… - Journal of Scientific …, 2023 - Springer
The well-suited discretization of the Keller–Segel equations for chemotaxis has become a
very challenging problem due to the convective nature inherent to them. This paper aims to …

[HTML][HTML] Numerical simulations for the chemotaxis models on surfaces via a novel characteristic finite element method

X **ao, X Feng, Y He - Computers & Mathematics with Applications, 2019 - Elsevier
In this paper, the chemotaxis partial differential equations models which describe the
movement by one community in reaction to one chemical or biological signal are given and …

[HTML][HTML] On the efficacy of a control volume finite element method for the capture of patterns for a volume-filling chemotaxis model

M Ibrahim, M Saad - Computers & Mathematics with Applications, 2014 - Elsevier
In this paper, a control volume finite element scheme for the capture of spatial patterns for a
volume-filling chemotaxis model is proposed and analyzed. The diffusion term, which …

Monotone combined edge finite volume–finite element scheme for anisotropic keller–segel model

G Chamoun, M Saad, R Talhouk - Numerical Methods for …, 2014 - Wiley Online Library
In this article, a new numerical scheme for a degenerate Keller–Segel model with
heterogeneous anisotropic tensors is treated. It is well‐known that standard finite volume …

Positive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system

C Cancès, M Ibrahim, M Saad - The SMAI journal of computational …, 2017 - numdam.org
In this paper, a nonlinear control volume finite element (CVFE) scheme for a degenerate
Keller–Segel model with anisotropic and heterogeneous diffusion tensors is proposed and …

Numerical analysis of a chemotaxis–swimming bacteria model on a general triangular mesh

G Chamoun, M Saad, R Talhouk - Applied Numerical Mathematics, 2018 - Elsevier
This paper is devoted to the numerical study of a model arising from biology, consisting of
chemotaxis equations coupled to Navier–Stokes flow through transport and external forcing …

[HTML][HTML] Numerical study of compositional compressible degenerate two-phase flow in saturated–unsaturated heterogeneous porous media

AS Saad, B Saad, M Saad - Computers & Mathematics with Applications, 2016 - Elsevier
We study the convergence of a combined finite volume–nonconforming finite element
scheme on general meshes for a partially miscible two-phase flow model in anisotropic …