Theoretical Study, Resolution, and Numerical Simulation of an Atmospheric Pollution Model: The Three-Dimensional Case

In this paper, a mathematical and numerical study is presented for a pollution model that describes the evolution of pollutant concentration within a cylindrical bounded domain of the atmosphere.The model represents a time-dependent problem in three-dimensional space, incorporating physical parameters relevant to atmospheric dynamics.The effectiveness of the proposed method is evaluated through analytical error estimates and numerical simulations.The results demonstrate not only the accuracy of the approximate solutions but also the stability and robustness of the method under various discretization settings.This confirms the finite element method as a reliable computational tool for modeling atmospheric pollution phenomena and sets the stage for future studies involving more intricate models or real-world environmental data.