Finite volume method for a Keller-Segel problem

• Main Authors: Messikh, C, Chowdhury, Md. Sazzad Hossien, Guesmia, A, Berkane, A
• Format: Conference or Workshop Item
• Language: English; English; English
• Published: IOP Publishing 2018
• Subjects: QA297 Numerical Analysis
• Online Access: http://irep.iium.edu.my/61803/7/61803-Finite%20volume%20method%20for%20a%20Kellar-Segel.pdf; http://irep.iium.edu.my/61803/8/61803-Finite%20volume%20method%20for%20a%20Keller-Segel%20problem-SCOPUS.pdf; http://irep.iium.edu.my/61803/19/61803_Finite%20volume%20method%20for%20a%20Keller-Segel%20problem_WoS.pdf; http://irep.iium.edu.my/61803/; http://iopscience.iop.org/article/10.1088/1742-6596/949/1/012015/pdf

In this paper, we are interested in the numerical simulation of the mathematical model of Keller-Segel Elliptic-Parabolic problem using finite volume scheme. The finite volume scheme is applied to the elliptic-parabolic model’s problem and we have shown under certain assumptions, the existence of a unique and positive approximate solution. Moreover, under adequate regularity assumption of the exact solution, the finite volume scheme is the first order accurate. A good agreement between our numerical simulation and the theoretical results has been obtained.