Stability and Convergence in Numerical Methods

This lecture covers the Lax-Milgram Lemma, consistency of order, stability, and convergence in numerical methods. It discusses the relationship between mesh size, stability, and convergence, emphasizing the importance of consistency of order. The lecture also explores the implications of stability on convergence, illustrating the concept through various examples. Additionally, it delves into the Dirichlet and Neumann boundary conditions, highlighting their significance in ensuring stability and convergence in numerical computations.