**Professors Paolo Secchi and Lucia Gastaldi**

**Civil and Environmental Engineering, Ingegneria per l'Ambiente e il Territorio**
**Academic Year 2019/2020**

Introduction and general information can be found here: in English
or in Italian

The program of the last year was:

**Mathematical models (3 CFU - Paolo Secchi): **

Convection-diffusion models of pollutants in a channel

Elements of mathematical analysis

Diffusion models

Introduction to problems in multi-dimensional domains

Heat equation

Fluid dynamics: Eulerian and Lagrangian coordinates, material derivative, transport theorem. Continuity equation, equations of motion. Perfect and viscous, compressible and incompressible fluids

Equations of motion in an elastic medium. Wave equations, Maxwell equations, pressure waves in a perfect compressible fluid

Diffusion model for a two-components fluid (e.g. diffusion of pollutants in water or air)

**Numerical methods (3 CFU - Lucia Gastaldi): **

Hyperbolic partial differential equations: Overview of linear transport equation, Finite difference schemes, Exercises

Boundary value problems: Poisson equation, Finite difference schemes, Exercises

The finite element method: Elliptic partial differential equation, Finite element method, Implementation: geometry, mesh, assembling

Numerical solution of the heat equation: Parabolic partial differential equation, Semi-discretization in space, Time advancing schemes, Computational aspects