Finite Element Space: Conforming Mesh

This lecture covers the concept of finite element spaces, focusing on conforming mesh construction and Galerkin error analysis. The instructor explains the importance of orthogonal scalar products and the Galerkin method in finding well-posed solutions. The lecture also delves into the error analysis with respect to the Galerkin method, emphasizing continuity and coercivity. Additionally, the lecture discusses the best approximation error and the quasi-optimal approximation method. The content progresses to the design of the space, detailing the construction of the finite element space and the partitioning process. The lecture concludes with a detailed explanation of the computational implications of conforming and non-conforming meshes.