2023-2024 / GCIV0185-7

Linear numerical methods in Civil and Geological Engineering


22h Th, 30h Pr, 30h Proj.

Number of credits

 Master of Science (MSc) in Civil Engineering5 crédits 
 Master of Science (MSc) in Geological and Mining Engineering5 crédits 
 Master of Science (MSc) in Geological and Mining Engineering (joint-degree programme with the "Université polytechnique de Madrid")5 crédits 


Laurent Duchene, Michel Pirotton

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

This course is an introduction to linear numerical methods and to their applications in the field of civil and geological engineering. It deals with finite differences, finite elements and finite volumes.

Learning outcomes of the learning unit

At the end of this course, the students will be able to solve a boundary value problem governed by differential equations with different methods: the finite element method, the finite difference method or the finite volume method.

One of the main objectives of this course is to make the students understand the basic principles of methods currently widely used in many software tools. The emphasis is put more on the theoretical fundamentals than on the application of such softwares.

In the list of KLO's/AA defined in the matrix available on https://www.programmes.uliege.be/cocoon/20182019/formations/descr/A2UCON01.html, this course focuses on the development of model suitable for solving problems in civil and geological engineering. In addition, the practial work, in small groups, focuses on the ability to analyse, communicate and report adequate results.

This course contributes to the learning outcomes I.1, I.2, II.1, III.1, III.2, III.3, IV.1, VI.1, VI.2, VI.3, VII.1, VII.2, VII.3, VII.4 of the MSc in civil engineering.

This course contributes to the learning outcomes I.1, I.2, II.1, III.1, III.2, III.3, IV.1, VI.1, VI.2, VI.3, VII.1, VII.2, VII.3, VII.4 of the MSc in geological and mining engineering.

Prerequisite knowledge and skills

The mathematical developments related to the numerical methods proposed in this course will rely on courses of mathematical analysis and numerical analysis.

Planned learning activities and teaching methods

This course consists in a theoretical part where the concepts are presented to the students and in a practical part where these concepts are applied by the students. These practical activities consist in the resolution of differential equation problems using the methods presented in the theoretical classes (finite elements, finite differences, finite volumes). 1D and 2D cases will be treated.

For these practical works, the students will have to deliver a report for each studied case. 

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course

Additional information:

The lectures are delivered face-to-face. The attendance to all lectures and practical works is mandatory. The lectures and practical courses will be taught in French. The slides will be in French and/or English.

For the practical works, a part of the work must be achieved during dedicated sessions (see the planning of the course). During these sessions, the students are invited to interact with the teacher to solve their problems. A part of the work must also be achieved by the students at home.

Recommended or required readings

The slides are available from the platform (https://mecaflu.argenco.ulg.ac.be/) as well as additionnal material.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )

Written work / report

Additional information:

The evaluation is based on the pratical work reports and on a written examination on the theory and/or on the direct application of the theory.This examination will be taken with the books closed and will cover both parts of the course: (1) finite differences and finite volumes, (2) finite elements.
The final mark of the course will be the average of the marks of the 2 parts.
All the lectures and the practical work sessions are mandatory.
In case of second session, the grade obtained for the reports will be kept unless the student wishes to present a new version of the practical works. In any case, the written exam is mandatory for the second session.

Work placement(s)

Organisational remarks and main changes to the course

The lectures are given during the first quadrimester, on Thursday morning.
Two additionnal half-days will be dedicated to practical works.


Theoretical lectures:
Laurent Duchêne, tel: 04/366 9328, l.duchene@uliege.be

Michel Pirotton, tel: 04/366 9536, michel.pirotton@uliege.be

Practical works:
Calogero Gallo, tel: 04/366 9835, cgallo@uliege.be

Laurence Defrere, tél: 04/366 9357

Association of one or more MOOCs