Theoretical Foundations of the Finite Element Method

Using finite element methods, we need to answer these questions: • What is the appropriate functional space V for the solution? • What is the appropriate weak or variational form of a differential equation? • What kind of basis functions or finite element spaces should we choose? • How accurate is the finite element solution? We briefly address these questions in this Chapter. Recalling that finite element methods are based on integral forms and not on the pointwise sense as in finite difference methods. We will generalize the theory corresponding to the pointwise form to deal with integral forms.