Norm Equivalence and Inverse Inequality

This lecture delves into the concept of norm equivalence on different spaces, particularly focusing on the relation between norms on K and K hat. The instructor explains the inverse inequality and its implications, highlighting why the inequality is not valid for functions in H1. By exploring the density of H1 in L2 and the behavior of gradients, the lecture demonstrates how the inequality contradicts the nature of functions in H1. The discussion extends to the condition number of the global stiffness matrix, emphasizing the challenges posed by fine mesh discretization. The lecture concludes with insights into error analysis using interpolation operators and the estimation of finite element method errors based on interpolation properties.