The weak formulation is indispensable for solving partial differential equations with numerical methods like the finite element method. Yet, the concept of the weak formulation is not easy to understand by just staring at the formulae. This video aims to visually explore the weak formulation following a simple example, i.e., the one-dimensional Poission equation with Dirichlet and Neumann boundary condition.
Video about the Finite Element Method: https://youtu.be/1wSE6iQiScg
0:00 Introduction
1:36 The Strong Formulation
8:08 The Weak Formulation
20:09 Partial Integration
23:21 The Finite Element Method
27:57 Outlook
Recommendations:
Finite Element Method - Numerical Analysis by Julian Roth https://www.youtube.com/watch?v=P4lBRuY7pC4&t=79s
A Brief Introduction to the Weak Form - Chien Liu https://www.comsol.com/blogs/brief-introduction-weak-form/
The Mathematical Theory of Finite Element Methods - S. C. Brenner and L. R. Scott https://link.springer.com/book/10.1007/978-0-387-75934-0
Music: Swans In Flight - Asher Fulero