A Petrov–Galerkin finite element method for simulating chemotaxis models on stationary surfaces

2020 ◽  
Vol 79 (11) ◽  
pp. 3189-3205
Author(s):  
Shubo Zhao ◽  
Xufeng Xiao ◽  
Jianping Zhao ◽  
Xinlong Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Chemotaxis Models ◽  
Element Method

scholarly journals Numerical study of Fisher's equation by a Petrov-Galerkin finite element method

1991 ◽  
Vol 33 (1) ◽  
pp. 27-38 ◽  
Author(s):  
S. Tang ◽  
R. O. Weber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Study ◽  
Galerkin Finite Element Method ◽  
Linear Diffusion ◽  
Galerkin Finite Element ◽  
Fisher’S Equation ◽  
Nonlinear Reaction ◽  
Fisher's Equation ◽  
Element Method

AbstractFisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by a Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are determined by the system itself and are independent of the initial values. Comparing with other studies, the numerical scheme used in this paper is satisfactory with regard to its accuracy and stability. It has the advantage of being much more concise.

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