Finite Element Development: Higher Order Basis Functions

This lecture covers the construction of higher-order basis functions in the context of finite element development, focusing on Lagrangian finite element families with linear and quadratic elements. It also discusses the numbering, basic functions, and storage optimization of higher-order elements, as well as the stiffness matrix, coordinate transformation, and components of the stiffness matrix. The lecture delves into digital integration techniques, including Gauss-Legendre quadrature rules, and their application in evaluating components of the elastic stiffness matrix. Additionally, it explores the precision of finite element models, error concepts, convergence factors, and asymptotic error estimates for solutions.