The course aims at providing an introduction to the design and the implementation of finite element methods to approximate the solution of partial differential equations. The students are expected to develop the following skills - being aware of the importance of the partial differential equations in the applied sciences, - understanding the notion of weak formulation of a partial differential equation, - understanding the principles and the basic properties of the finite element methods, - knowing the general structure of a code implementing a finite element method, navigating it and being able to modify it according to specific requirements, and - being able to represent, analyze and interpret the numerical results.
Course Prerequisites
- Linear algebra: vectors, matrices, vector spaces, bases
- Calculus: differential and integral calculus for multivarite functions
- basic knowledge of python
Teaching Methods
- Lectures - Individual or group solution of exercises - Thematic seminars
Assessment Methods
Carrying out of a project and oral examination
Texts
Main references - Lecture notes provided by the lecturer
Advanced references - A. Ern, J.-L. Guermond, Theory and Practice of Finite Elements, 2004 - A. Quarteroni, Modellistica Numerica per Problemi Differenziali, 2012
Contents
1. Partial differential equations 2. Galerkin method 3. The FEniCS toolbox 4. Meshes 5. Finite elements 6. Implementation 7. Test cases 8. Assembling 9. Linear solvers 10. Error 11. Further examples
Course Language
Italian
More information
Any question related to the course can be discussed with the lecturer, either in person or online, upon request. The lecturer will provide lecture notes and solutions of the exercises. Further material could be made available upon request.
