Variational Formulation: Weak Formulations & Galerkin

This lecture covers the concept of weak formulations, Galerkin method, and variational formulations in the context of finite element methods. It discusses the construction of basis functions, associated with different types of vertices, and the modification of the right-hand side. The lecture also explores the Dirichlet boundary conditions, Lipschitz domains, and the Poincaré inequality. Additionally, it delves into the properties of H-seminorms, the link between different function spaces, and the importance of the Lax-Milgram Lemma in ensuring well-posed problems.