Course syllabus

Course code: FSF3571 HT25
Credits: 4.5 hp
Level: Advanced (PhD level)
Duration: 3 weeks of full-time study

Course Aim:
The aim of this course is to provide participants with an introduction to the theory, analysis, and implementation of Cut Finite Element Methods (CutFEM). The course emphasizes both the mathematical foundations and practical aspects of unfitted finite element techniques for solving partial differential equations on complex geometries and evolving domains.

Prerequisites:
Participants are expected to have basic knowledge of the standard Finite Element Method (FEM), including familiarity with weak formulations of partial differential equations.

Learning Outcomes:
After completing the course, participants should be able to:

  • Explain the fundamental principles behind CutFEM and unfitted finite element methods.

  • Formulate and analyze CutFEM for basic model problems.

  • Discuss stabilization techniques and integration over cut elements.

  • Critically read and present current research papers in the field.

Course Content:
The course covers:

  • Introduction to CutFEM and applications to model problems.

  • Analysis of CutFEM for second-order symmetric problems.

  • Numerical integration on cut elements.

  • Weak and strong stabilization for bulk and surface problems.

  • Weak imposition of interface and boundary conditions using Lagrange multiplier and stabilization methods such as Nitsche's method. 

  • CutFEM techniques for time-dependent and moving domains.

Teaching Format:
The course consists of six lectures, supplemented by independent reading, one research presentation by each participant, and attendance at at least one research talk within the Interfaces and Unfitted Discretization Methods program at the Institute Mittag-Leffler.
Some software and computational tools will be made available to support numerical experimentation.