This course is discontinued

INF9691 – Advanced finite element methods

Schedule, syllabus and examination date

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Course content

Finite element methods provide a general and powerful framework for solving ordinary and partial differential equations. This course is a continuation of the introductory course INF5680: Introduction to Finite Element Methods and focuses on the automation of the finite element method, adaptivity and stabilization.

The following topics are studied in this course: efficient tabulation of finite element basis functions, efficient representation of computational meshes, efficient computation of the element tensor (element stiffness matrix), tensor representation of multilinear forms, finite element code generation, error estimation by duality, stability factors, variational crimes, mixed methods, the Babuska-Brezzi inf-sup condition, stabilization, application to Stokes, Navier-Stokes and systems of nonlinear convection-diffusion-reaction equations.

Learning outcome

Students will learn advanced topics and techniques in finite element methods and how to implement and apply these techniques to solve nonlinear systems of ordinary and partial differential equations.


PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.


Recommended previous knowledge

It is assumed that the student has taken the course INF5680 Introduction to Finite Element methods or has a similar background. It is also assumed that the student has some experience with Python (or is willing to learn).


A number of advanced topics in finite element methods will be presented in an introductory series of lectures. Students should then choose one of these topics to study in detail. The students have to make a mandatory project plan, if this is not accepted, the student may not take the final exams.

In addition, each PhD student is expected to give an oral presentation on a topic of relevance (chosen in cooperation with the lecturer). The presentation has to be approved by the lecturer for the student to be admitted to the final exam.

We will make extensive use of FEniCS ( as the basic tool for generation of finite element meshes, finite element basis functions, finite element assembly, linear algebra and plotting.


The grade is based upon an individual written project report (counts 70%) and an individual presentation (counts 30%). All parts must be completed in the same semester.

Examination support material

All resources allowed on the written report.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Resit an examination

This subject does not offer new examination in the beginning of the subsequent term for candidates who withdraw during an ordinary examination or fail an ordinary examination. For general information about new examination, see /studier/admin/eksamen/sykdom-utsatt/mn/index.html and

General exam information at the Faculty of Mathematics and Natural Sciences


Note that the first lecture is mandatory.

Facts about this course






Every autumn


Every autumn

Teaching language