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This lecture covers the concept of streamline diffusion and diffusion in the context of numerical methods, emphasizing the importance of fully consistent approaches. The instructor discusses the challenges of discretization and the need for solutions that do not oscillate. Various numerical techniques, such as SUPG and GALS, are explored to ensure accurate and stable results. The lecture also delves into the application of Petrov-Galerkin methods and the significance of consistency in solving continuous problems.