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SG243

6ICG283

Duration: 21 hours

ECTS Credits: 2  

Semester: S8

Course Title:

Computational solution 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:

Give an introduction to the numerical solution of Partial Differential Equations arising in many applied sciences and engineering problems

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
  • Aucune étiquette