This thesis is about the numerical simulation and optimization of the alumina repartition in the bath of an aluminium electrolysis pot. A mathematical model is set up which contains the feeding of alumina particles to the bath, the dissolution of the particles, the motion of the alumina in the bath, and the consumption of the alumina by electrolysis. The arising convection-diffusion equations are solved using stabilized finite elements. Different weak formulations of the convection-diffusion equation are compared and we find a formulation which ensures mass conservation even if the velocity field is not divergence free. A comparison of the complete numerical simulation with real world experiments is carried out, showing that the numerical results are in very good agreement with the measured values. In a second part we optimize the feeding of the particles, with the aim of getting a more uniform distribution of the alumina concentration in the bath. A mathematical model of the optimization problem is proposed and subsequently solved using particle swarm optimization and Newton's method.