The Finite Element Method (SF2561), 7.5hp, Fall 2014

[Work in progress]

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The Finite Element Method

The Finite Element Method (FEM) is a numerical method for solving general differential equations. FEM was first developed for elasticity and structural analysis, but is today used as a universal computational method in all areas of science and engineering, including fluid mechanics, electromagnetics, biomechanics and financial mathematics. The mathematical framework of FEM is well developed, which allows for detailed estimation of the discretisation error and efficient adaptive algorithms that minimise the computational cost, and many FEM software implementations are available, both commercial and open source. This course will cover the theory of FEM, basic algorithms, and practical aspects including software implementation. 

Examples of FEM simulations using the open source software FEniCS.

Practical information

The course consists of:

• 9 lectures
• 2 laboratory sessions
• 6 exercise sessions

Course goals

The goal of this course is to give basic knowledge of the theory and practice of the finite element method and its application to solve the partial differential equations of physics and engineering sciences. The purpose is to give a balanced combination of theoretical and practical skills. The theoretical part is mainly concerned with the derivation of finite element formulations, estimating the discretisation error and to use error estimates to adaptively refine the mesh. The practical part deals with computer implementation of the method: matrix and vector assembly, numerical integration, etc.

Course PM

Project PM

Course leader

Johan Hoffman 

Office hours

Mondays 9:00-10:00 (Office 4429, Lindstedtsvägen 5) 

Literature

Course book (CDE): Eriksson, Estep, Hansbo, Johnson, "Computational Differential Equations", Studentlitteratur, (ISBN ISBN 91-44-49311-8), 1996. [Bokus] [Studentlitteratur]

Software

Puffin (simple Matlab/Octave FEM software)

FEniCS (advanced Python/C++ FEM software)

Extra material

Further reading

Add-on studies

DN2295 Project Course in Scientific Computing (talk to course leader) 

DN2275 Advanced Computation in Fluid Mechanics

MSc projects

Preliminary week plan

Week 1 

Lecture 1 (Mon Sep 1, 13-15, V01)

Lecture 2 (Tue Sep 2, 13-15, E32)

Week 2

Lecture 3 (Mon Sep 8, 15-17, E32)

Lab 1 (Fri Sep 12, 13-15, 5O1Spe)

Week 3

Lecture 4 (Tue Sep 16, 15-17, E32)

Lab 2 (Wed Sep 17, 10-12, 5O1Spe)

Exercise 1 (Fri Sep 19, 13-15, D34)

Week 4

Lecture 5 (Thu Sep 15, 14-16, L51)

Lecture 6 (Fri Sep 16, 14-16, E35)

Week 5

Lecture 7 (Mon Sep 29, 10-12, D34)

Exercise 2 (Tue Sep 30, 10-12, E32)

Week 6

Lecture 8 (Mon Oct 6, 10-12, V01)

Exercise 3 (Wed Oct 8, 8-10, V21) 

Exercise 4 (Fri Oct 10, 13-15, E51) 

Week 7

Lecture 9 (Mon Oct 13, 10-12, E36)

Exercise 5 (Wed Oct 15, 8-10, V01)

Exercise 6 (Fri Oct 17, 13-15, D34)

Week 8

Week 9

Written exam (Thu Oct 30, 8-13, E32)