Variational Methods of Approximation

Abstract

In this chapter, we describe several of the more popular variational methods for the approximate solution of boundary-and initial-value problems. For ease in presentation, we confine our attention to linear problems, and most of what we present has to do with elliptic boundary-value problems. In particular, we discuss interpolation properties of finite element methods, existence and uniqueness of solutions to the approximate problem, and convergence and error estimates of finite element methods for linear elliptic problems. More detailed accounts of linear elliptic problems can be found in [47, 109, 135].