Lecture
This lecture covers different discretization schemes for steady convection-diffusion problems, such as upwind differencing, linear upwind differencing, and quadratic upstream interpolation. It explains the concepts of boundedness, transportiveness, and conservativeness, as well as the accuracy and stability of each scheme. The lecture also introduces the deferred correction approach to handle negative coefficients and discusses the MUSCL scheme for unstructured meshes. Additionally, it presents the total-variation diminishing (TVD) schemes to achieve higher-order accuracy without introducing new extrema.