LEFORT, M. Albéric (0009) Approches numériques des problèmes de défauts dans les équations de réaction-diffusion à coefficients oscillants PFE - Project Graduation, ENSTA.



We study in this report the reaction-diffusion equation, with oscillating coefficients. As in any multiscale problem, the numerical approximation by standard methods of the solution uε requires too expensive discretizations when ε is small. We have to adopt other approaches. Thus we study in a first step the homogenization of this equation, in the periodic case. Some of these results will be rigorously proved, others will remain only heuristic. We then implement a numerical simulation using the Multi-scale Finite Element Method ("MsFEM"). We use some of the results of the homogenization of the equation to infer the best approach. This implementation will be performed in the one dimensional case to reduce computational costs.

Item Type:Thesis (PFE - Project Graduation)
Uncontrolled Keywords: Partial Differential Equations, Periodic Homogenization, Multi-scale Finite Element Method
Subjects:Mathematics and Applications
ID Code:9250
Deposited By:Alberic Lefort
Deposited On:05 juin 2023 10:10
Dernière modification:05 juin 2023 10:10

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