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SG243

6ICG283

Duration: 21 hours

ECTS Credits: 2  

Semester: S8

Course Title:

Numerical Computational solution of to Partial Differential Equations and applications

Person(s) in charge:

Xavier ANTOINE, Professor, xavier.antoine@univ-lorraine.fr

Keywords: Partial differential Equations, Numerical Methods, Finite differences, Finite Elements

Prerequisites: the partial differential equations course. Basic knowledge in numerical analysis and MATLAB would be helpful.

Objective:

Program and contents:

The goal of this course is to give an introduction to the numerical solution of Partial Differential Equations arising in many applied sciences and engineering problems. We mainly focus on Finite Element Methods as well as Finite Difference Methods. We develop different applications for the solution of equations related to engineering problems. Some examples are related to wave equations, heat equations, elliptic equations, models coming from financial mathematics, two-dimensional problems… A large part of the course is to explain how to concretely develop a professional finite element or finite difference code. Examples will be considered in Matlab using e.g. the dedicated PDE Toolbox.

Content

• Chapter 1: The Finite Element Method: from theory to codes
• Chapter 2: The Finite Difference Method: essential elements

Abilities: 

Levels

Description and operational verbs

Know 

Understand 

Apply 

Analyze 

Summarise

Evaluate

Evaluation:

•  Written test

•  Continuous Control

•  Oral report

•  Project

•  Written report