• Studies
• Courses
• • INF5691

INF5691 - Advanced finite element methods

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 outcomes

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.

Admission

Students at UiO must apply for courses in StudentWeb.

International applicants, if you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

The examination in this course is not available for external candidates. Only students admitted to the course may sit for the examination.

Prerequisites

Recommended prior 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).

Teaching

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. Rules for mandatory assignments.

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

Exam information

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. General information about the examination.

Exam resources

All resources allowed on the written report.

Assessment and grading

Course grades are awarded on a descending scale using alphabetic grades from A to E for passes and F for fail. Read more about the grading system .

Possibility of make-up exams and re-takes

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 http://www.mn.uio.no/studier/admin/eksamen/utsatt-og-ny-eksamen/index.html and http://www.mn.uio.no/english/studies/admin/examination/retaking-examinations/

Withdrawing from exams and limits on re-takes

A student can sit for this exam up to 3 times. If a student wishes to withdraw from the exam, s/he must do this in StudentWeb at least two weeks prior to the first day of the exam. Failure to do so will be counted as one of the three opportunities to sit for the exam.

Other information

It is strongly recommended to attend the first lecture since it will be given important information.

Contact us