Direct Problem for Gas Diffusion in Polar Firn for Variable Gas Volume Fractions

Abstract

Studying atmospheric gas concentrations in firn helps reconstruct historical climate conditions, crucial for understanding climate change and global warming. In this thesis, we study a time-dependent partial differential equation that models gas concentrations with variable gas volume fractions both theoretically and numerically, in line with the work of Moufawad, Nassif, and Triki (2023). The theoretical part consists of using semi-variational formulation of the problem and proving existence and uniqueness of its solution. As for the numerical part, we similarly discretize using Finite Element in space and Finite difference in time leading to a system of linear equations to be solved at each time step. Finally, we implement and test the developed algorithms using MATLAB, which demonstrates robust and successful results.