The document provides an introduction to the finite element method. It compares the finite element method to classical methods and the finite difference method. Some key differences highlighted include: - Classical methods obtain exact solutions for simple cases while finite element methods obtain approximate solutions for all problems. - Finite element methods can handle problems with complex geometry, multi-materials, and non-linearities, while classical methods have difficulties with these. - Finite difference methods make point-wise approximations while finite element methods make piece-wise approximations, allowing for continuity along element boundaries. - Finite element methods can evaluate values between nodes through interpolation, while finite difference methods only provide values at nodes.