Courses

Numerical Methods for Partial Differential Equations

This course offers a comprehensive exploration into the numerical solution of Partial Differential Equations (PDEs), with a special emphasis on Finite Element Methods (FEMs).ย 

The curriculum explores the construction of Finite Element Spaces and polynomial approximation theory in Sobolev Spaces, to establish classical convergence theorems for elliptic problems. The course covers as wellย “variational crimes” and mixed methods, expanding the theory’s applicability to a wider range of PDEs. The theory is complemented with practice, using both front lectures and flipped classroom laboratories, working on implementations based on C++ using the deal.II library.

Key principles such as consistency, stability, convergence, and adaptivity will be examined in detail, offering guidelines for the selection and implementation of numerical methods suitable for the solution of a broad spectrum of partial differential equations.

Numerical Methods for PDEs

Calcolo numerico

This is the second module of the course “Analisi Numerica 2 e Calcolo Numerico” for Ingegneria dell’Energia of the University of Pisa.
The course focuses on teaching the fundamental techniques of numerical analysis. Students will learn about error analysis, machine arithmetic, polynomial interpolation, integral approximation, numerical approximation of the solutions to nonlinear equations, methods for solving systems of linear equations, and numerical methods for the solution of initial boundary value problems. 

The course is in Italian, and it is generally in the second semester, on Tuesday and Wednesday morning.

Calcolo Numerico