Functional Analysis, Boundary Value Problems and Finite Elements

This chapter presents, first, an overview of the mathematical tools required to undertake studies of the well-posedness of linear boundary value problems and their approximations by finite elements. In the remainder of this work, these tools are used to examine the existence and uniqueness of solutions to weak boundary value problems, and convergence of finite element approximations. The emphasis is on second-order partial differential equations, with the governing equations for linear elasticity being the key model problem.