Finite Element Method: Weak Solutions

This lecture introduces the concept of weak solutions in the context of the finite element method, covering topics such as the Galerkin method, classical solutions, verification of weak solutions, and the Sobolev space theory. The lecture progresses from the basic concepts to the application of Poincare inequality and the Coercivity principle, emphasizing the importance of continuity and the Cauchy-Schwarz inequality. The instructor explains how these concepts are crucial for understanding the behavior of solutions in the context of distribution and compact support.