Uppsala University
Department of Information Technology
Scientific Computing
Applied Finite Element Methods

Applied Finite Element Methods

Finite element solution of Compressible Euler equations. Strong shocks and contact lines.


In this course you will learn the basic knowledge of the theory, practice and implementation of finite element methods to the partial differential equations of physics and engineering sciences. The main purpose is to give a balanced combination of theoretical and practical skills. The theory part gives you knowledge on the derivation of finite element formulations, a priori and a posteriori error estimates, methods and algorithms of adaptive mesh refinements, computer implementations of the finite element discretizations: element matrices, assembly process, numerical integration, local mesh refinement, etc. The practical part of the course helps you to learn to program finite element discretizations in Matlab in 1D and 2D. You will also learn to solve realistic partial differential equations in the open source computational science software FEniCS.

Syllabus in pdf


Lecturer: Murtazo Nazarov
Room: 2421
Phone: 018-471 6287
E-mail: murtazo(DOT)nazarov(AT)it(DOT)uu(DOT)se
Office hours: Fridays 10:15-11:00, or by appointments


[LB] Larson, M.G., Bengzon, F. The Finite Element Method: Theory, Implementation, and Practice. Department of Mathematics, Umea University 2009.

[EEHJ] K. Eriksson, D. Estep, P. Hansbo, C. Johnson. Computational Differential Equations. Studentlitteratur, ISBN ISBN 91-44-49311-8.

[J] C. Johnson. Numerical Solution of Partial Differential Equations by the Finite Element Method.

[EG] Alexandre Ern, Jean-Luc Guermond. Theory and Practice of Finite Elements. ISBN 978-0-387-20574-8.

In this course we will mainly use [LB].

Course content

There will be 12 lectures, 7 exercise classes, and 4 laborations.


There will one mandatory project and one written exam.
Project: 2 points
Final: 3 points

Scholastic Dishonesty

Students may work together and discuss the homework problems with each other. Copying work done by others is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. For more information on university policies regarding scholastic dishonesty, see the University of Uppsala's policy at http://www.it.uu.se/edu/fusk.pdf .

Students with Disabilities:

According to the University regulation all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you need help or want to get more information about it please contact the University of Uppsala's services for students with disabilities.