• 096624 - MATHEMATICAL METHODS FOR ENGINEERING [2]

PROGRAM (Numerical Methods) - Cod. 096624

Many physical phenomena are formulated in terms of partial differential equations e.g. the diffusion of heat,  electrical conduction, propagation of waves. In this part of the course, we will analyze and implement the finite element method (FEM) for the numerical approximation of elliptic, parabolic and wave equations. This will also require the study of the basic numerical algorithms aiming at solving linear systems, approximating functions and integrals, solving systems of ordinary differential equations. The last part of the course will be devoted to the numerical solution of a model control problem.

Syllabus

A. Basic tools of Numerical Analysis

Numerical methods for the solution of linear systems: direct and iterative schemes. Approximation of functions: polynomial interpolations. Numerical Integration: Newton-Cotes Formulae. Numerical methods for the solution of ordinary differential equations: Implicit and Explicit Euler.

B. The Finite Element Method for partial differential equations

Finite element approximation of elliptic problems: variational formulation, algebraic formulation and error estimates.  Finite element approximation of parabolic and wave equations: variational formulation, algebraic formulation and error estimates. A brief introduction to the numerical solution of control problems (for example stemming from optical tomography).

 There will be only a written exam.

e-book of the italian version available.