The finite element method has given us the ability to solve PDEs when analytical solutions are out of reach. These numerical techniques have been developed and perfected over the last few decades and are now ubiquitous throughout engineering. Problems are mostly solved for linear problems are simple perturbations of linear problems; whereas nonlinear and multiphysics problems are still active areas of research.

• Introductory to higher level mathematics: Applied Functional Analysis
• Learn the mathematics describing PDEs: Functional Analysis for the Applied Mathematician
• The numerical analysis of finite elements: Mathematical Theory of Finite Elements
• For implementation of finite elements: The Finite Element Method