History of the Finite Element Method – Mathematics Meets Mechanics – Part II: Mathematical Foundation of Primal FEM for Elastic Deformations, Error Analysis and Adaptivity

Abstract

This chapter treats the history of mathematical foundation of primal FEM, especially a posteriori error estimates and adaptivity, based on functional analysis in Sobolev spaces. This is of equal importance as the creation of multifarious computational methods and techniques in engineering and computer sciences. BVPs for linear elliptic PDEs, mainly the Lamè equations for linear static elasticity are treated.