Introduction to the Finite Element Method

Detailes on our lecture "Introduction to the Finite Element Method"

Contents

  • Fundamental concepts of discretization and approximation
  • Mathematical modelling with partial differential equations
  • Strong and weak forms of PDEs (variational principle, principle of virtual work, Ritz & Galerkin methods, method of weighted residuals)
  • Isoparametric element formulations for linear continuum elements in heat transfer and structural mechanics
  • Numerical integration and solution of sparse systems linear of equations
  • Enforcement of boundary conditions
  • Mathematical foundations of FEM and convergence analysis (h- & p-refinement, error estimation and adaptivity)
  • Locking phenomena, mixed methods and reduced integration
  • Modal analysis and time-integration methods for dynamics
  • Structural beam and truss elements

Winter term 2025-2026

Due to Prof. Weeger's research semester, the lecture will not be offered in the winter semester 2025/26. Nevertheless, there will be a written exam in March 2026, for which students can prepare using the materials provided in the Moodle course (videos, lecture slides, exercises, and supplementary materials). In addition, there will be office hours for summaries, questions and answers well in advance of the exam. Further information will be announced in the Moodle course.

Details

Lecture name Introduction to the Finite Element Method
Module no. 16-73-5030
Term Winter
Lecturer Prof. Dr. rer. nat. O. Weeger
Responsible assistant --
Credit points 6
Contact hours Lecture: 3 SWS
Recitation: 1 SWS
Lecture & recitation dates --
Start of lectures --
Room --
Language English (Summaries and lecture script in German)
Examination Written exam on March 6, 2026
Further information and materials see TUCaN and Moodle

Usability of this module

  • Master in Mechanical Engineering (Electives Area II)
  • Master in Aerospace Engineering
  • Master in Computational Engineering
  • Master in Mechanics
  • Master in Business Administration/Industrial Engineering – specialising in Mechanical Engineering
  • Master in Mechatronics