Finite Element Method: Weak Formulation and Galerkin Method

This lecture covers the weak formulation of the problem in the context of the Finite Element Method, focusing on adapting the weak form to different boundary conditions, including non-homogeneous and Neumann conditions. It also explores the Galerkin method for discretizing the weak form, approximation of real and virtual displacements, and the application of finite elements in solving linear systems of equations. The instructor discusses the elementary stiffness matrices, global stiffness matrix, and the system of linear equations, providing examples of their application in analyzing a prismatic bar with discontinuities. Additionally, the lecture delves into the concept of volume elasticity, thermal heat, and various physical laws governing different phenomena.