VARIATIONAL METHODS IN COMPUTATIONAL MECHANICS

Course objectives

The objective of the course is to introduce the students to the variational deduction of many physical models of Engineering interest. Using variational approaches, the students will learn not only to deduce rigorous mathematical models in both solid and fluid mechanics, but also to manage the numerical tools for their solutions.

Channel 1
STEFANO VIDOLI Lecturers' profile

Program - Frequency - Exams

Course program
The course introduces to main modern variational tecniques used to formulate and computationally solve problem in fluid and solid mechanics Strong and weak (variational) forms of PDEs problems. Basic introduction to functional analysis: normed spaces, Hilbert spaces, bases. Boundness and coecitivity of linear differential operators. Variational formulation of some Continuum Mechanics problems for both fluids and solids. Discretization techniques. Galerkin approximations and error estimates: the case of the Finite Element Method. Examples and project proposals in the FENICs framework.
Prerequisites
Basic notions for the treatement of ODEs and PDEs. Calculus on vector fields: gradient, divergence, curl. By parts integration and basic theorems in Anaysis. Basic notions in Solids and fluid mechanics
Books
On the website https://sites.google.com/a/uniroma1.it/stefanovidoli/insegnamenti a preliminary draft of the course material is available.
Teaching mode
Lectures and computer-assisted examples The main programs used will be Mathematica and FENICS
Frequency
Even if not necessary, following the course is warmly suggested
Exam mode
Homework on a specific course argument and oral exam
Bibliography
Dacorogna: Introduction to Calculus of Variations, Imperial College Press 2004 Roman: Some modern mathematics for physicists and outsiders. Pergamon 1975 Ciarlet: Mathematical elasticity, Elsevier 2000 Ciarlet: The finite element method for elliptic problems, SIAM 2002
Lesson mode
Lectures and computer-assisted examples The main programs used will be Mathematica and FENICS
  • Lesson code10589635
  • Academic year2025/2026
  • CourseMechanical Engineering
  • CurriculumMeccanica Computazionale Pierre and Marie Curie University (Percorso valido anche per coloro che partecipano al percorso internazionale italo-francese finalizzato al conseguimento del doppio titolo)
  • Year1st year
  • Semester1st semester
  • SSDICAR/08
  • CFU6