Finite Element and Boundary Element Methods

Abstract

In this chapter, finite element and boundary element methods are introduced. Functional analysis plays important role to reduce the problem in discrete form amenable to computer analysis. The finite element method is a general technique to construct finite-dimensional spaces of a Hilbert space of some classes of functions such as Sobolev spaces of different orders and their subspaces in order to apply the Ritz and Galerkin methods to a variational problem. The boundary element method comprises transformation of the partial differential equation describing the behavior of an unknown inside and the boundary of the domain into an integral equation relating to any boundary values, and their finding out numerical solution.