Introduction to Finite Element Analysis

Abstract

In the previous two chapters we have formulated and analyzed the primal and dual variational formulations of the elastoplasticity problem. Later on, we will study various numerical methods to solve the variational problems. In all the numerical methods to be considered, we will use finite differences to approximate the time derivative and use the finite element method to discretize the spatial variables. The finite elemfent method is widely used for solving boundary value problems of partial differential equations arising in physics and engineering, especially solid mechanics. The method is derived from discretizing the weak formulation of a boundary value problem. The analysis of the finite element method is closely related to that of the weak formulation of the boundary value problem.