Finite Elements Method: Error Estimation

This lecture covers the estimation of a priori error in the finite elements method, focusing on convergence analysis, orthogonality, boundary conditions, weak formulations, and virtual displacements. It also discusses the equivalence of strong and weak formulations, integration by parts, and the exact weak form. The lecture further explores the best approximation of the solution in a subspace, error functions, and optimal precision. Examples and applications of the method are provided, along with discussions on superconvergence, error norms, energy standards, and a priori error estimates with linear basis functions.