Finite volume methods: foundation and analysis
Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlap** control volumes. Degrees of …
decomposition of a problem domain into nonoverlap** control volumes. Degrees of …
Keller-Segel chemotaxis models: A review
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 …
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
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 …
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
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 …
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 …
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
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 …
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
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 …
heterogeneous anisotropic tensors is treated. It is well‐known that standard finite volume …
Positive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system
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 …
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
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 …
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
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 …
scheme on general meshes for a partially miscible two-phase flow model in anisotropic …