I Finally Understood The Weak Formulation For Finite Element Analysis

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 Poisson equation with Dirichlet and Neumann boundary condition.

I am using the word ansatz for the assumed form of the solution function u. Although ansatz is a German word, it is also frequently used in English, especially in the mathematical context. https://en.m.wikipedia.org/wiki/Ansatz

Video about the Finite Element Method:    • Finite Element Method Explained In 3 Level...  

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    • Finite Element Method  
A Brief Introduction to the Weak Form - Chien Liu https://www.comsol.com/blogs/brief-in...
The Mathematical Theory of Finite Element Methods - S. C. Brenner and L. R. Scott https://link.springer.com/book/10.100...

Music: Swans In Flight - Asher Fulero