Construction of Finite Elements

This lecture covers the construction of finite elements for the Darcy problem, focusing on discretizations and the choice of finite element spaces. The instructor explains the importance of well-posedness and the inf-sup condition, highlighting the challenges in selecting appropriate finite elements. Various modes of convergence and the impact of the inf-sup condition on the solution are discussed, emphasizing the difficulty in achieving continuity across edges. The lecture concludes with a detailed examination of the properties and constraints of the constructed finite elements.