Convection-Diffusion Equations

This lecture covers the topic of convection-diffusion equations, focusing on the analysis of the Poincare constant, continuity, and interpolation error. The instructor explains the impact of different spaces and singular perturbations in solving the convection-diffusion problem. Emphasis is placed on understanding the behavior of the solutions under various conditions, such as high Peclet numbers and boundary conditions. The lecture also delves into the challenges of upwind fixes and the oscillating nature of the Peclet number, providing insights into strategies for addressing these issues.