Paper Info
Title
A Petrov-Galerkin finite element method for simulating chemotaxis models on stationary surfaces.
Abstract
In this paper, we present a Petrov–Galerkin finite element method for a class of chemotaxis models defined on surfaces, which describe the movement by one community in reaction to one chemical or biological signal on manifolds. It is desired for numerical methods to satisfy discrete maximum principle and discrete mass conservation property, which is a challenge due to the singular behavior of numerical solution. Thus a Petrov–Galerkin method is combined with an effective mass conservation factor to overcome the challenge. Furthermore, we prove two facts, this method maintains positivity and discrete mass conservation property. In addition, decoupled approach is applied based on the gradient and Laplacian recoveries to solve the coupling system. The relevant stability analyses is provided. Finally, numerical simulations of blowing-up problems and pattern formulations demonstrate the effectiveness of the proposed method.
Year
DOI
Venue
2020
10.1016/j.camwa.2020.01.019
Computers & Mathematics with Applications
Keywords
DocType
Volume
Surface chemotaxis models,Surface finite element method,Petrov–Galerkin method,Positivity preservation,Mass conservation
Journal
79
Issue
ISSN
Citations 
11
0898-1221
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Shubo Zhao100.68
Xufeng Xiao212.38
Jianping Zhao300.34
Xinlong Feng413522.33