FINITE ELEMENT APPLICATIONS IN MATHEMATICAL PHYSICS

Abstract

This chapter discusses finite element applications in mathematical physics. The objective is to show the relationship of the finite element method to a variety of classical methods of approximate analysis, to demonstrate techniques for formulating various types of finite element models of boundary and initial value problems, and then, to establish the generality and flexibility of the method, to discuss a broad range of problems in mathematical physics in which the method has been applied successfully. The finite-element method is a systematic technique for constructing the basis functions ωi(x) for Ritz–Galerkin approximations for irregular domains. Apart from a number of other advantages, the method overcomes all of the traditional disadvantages of Ritz–Galerkin procedures. The basis functions ωi(x) are generated in a straightforward and systematic manner, irregular domains and mixed boundary conditions are easily accommodated, the resulting equations describing the discrete model are generally well-conditioned, and the method is exceptionally well suited for implementation via electronic computers.