High-Order FEM

General information:

Lecture and exercise notes can be retrieved at Stud.Ip.


  1. Introduction
  2. Motivation
  3. Hierarchic shape functions
  4. Mapping functions
  5. Computation of element matrices, assembly, constraint enforcement and solution
  6. Convergence characteristics
  7. Mechanical models and finite elements for thin-walled structures
  8. Computation of thin-walled structures
  9. Error estimation and hp-adaptivity
  10. High-order fictitious domain methods


Students are able to

  • give an overview of the different (h, p, hp) finite element procedures.
  • explain high-order finite element procedures.
  • specify problems of finite element procedures, to identify them in a given situation and to explain their mathematical and mechanical background.


Students are able to

  • apply high-order finite elements to problems of structural mechanics.
  • select for a given problem of structural mechanics a suitable finite element procedure.
  • critically judge results of high-order finite elements.
  • transfer their knowledge of high-order finite elements to new problems.