# Coursebooks 2016-2017

## Introduction to the finite elements method

Quarteroni Alfio

English

#### Summary

Introduction to the finite element method for the numerical solution of differential problems in one or several dimensions. Mathematical aspects, numerical algorithms, application to diffusion, transport and reaction problems of physical relevance

#### Content

- Examples of elliptic, parabolic and hyperbolic problems
- Weak formulation
- Finite element approximation
- Stability and convergence analysis for elliptic problems
- Discretization by finite differences in time and finite elements in space of time-dependent problems
- Temporal stability analysis

- Finite element coding by MATLAB

#### Keywords

finite element method

stability, convergence, error estimates

solution of large dimensional systems

application to physics and engineering

#### Learning Prerequisites

##### Required courses

Analyse I et II

Analyse Numerique

##### Recommended courses

Cours prérequis indicatifs

Programmation

Analyse III

##### Important concepts to start the course

differential equations

linear systems

#### Learning Outcomes

By the end of the course, the student must be able to:
• Choose an appropriate method
• Interpret the results of a computation in light of theory
• Assess / Evaluate numerical errors
• Prove mathematical properties of the finite element method
• Apply the finite element method to solve problems of physical relevance

#### Transversal skills

• Use a work methodology appropriate to the task.
• Communicate effectively with professionals from other disciplines.
• Give feedback (critique) in an appropriate fashion.

#### Teaching methods

Ex cathedra lecture and exercises in classroom

#### Expected student activities

Presence and participation to class

To solve the exercises

To solve physical problems on a computer

written exam

#### Supervision

 Office hours Yes Assistants Yes

#### Prerequisite for

Approximation numerique des équations aux dérivées partielles

(Numericalapproximation of partial differential equations)

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German