Review of Classical FEM Formulations and Discretizations

Abstract

The objective of this first chapter is to recall the basics of Finite Elements for simple problems, here, the steady-state and linear elasticity problems, in order to use it as a solver for the localization problems required in computational homogenization in the next chapters. We do not intend to provide a complete framework on FEM here, but present a short introduction and practical aspects which can be used to directly implement a FEM program. For more in-depth about FEM formulations, we refer to classical books on Finite Elements such as [1,2,3,4] for linear problems and [5, 6] for nonlinear problems.