Module Description

Module: High-Order FEM


High-Order FEMLecture3Summer Semester
High-Order FEMRecitation Section (large)1Summer Semester

Module Responsibility:

Prof. Alexander Düster

Admission Requirements:


Recommended Previous Knowledge:

Mathematics I, II, III, Mechanics I, II, III, IV

Differential Equations 2 (Partial Differential Equations)

Educational Objectives:

Professional Competence

Theoretical Knowledge

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.

Personal Competence

Social Competence

Students are able to
+ solve problems in heterogeneous groups and to document the corresponding results.


Students are able to
+ assess their knowledge by means of exercises and E-Learning.
+ acquaint themselves with the necessary knowledge to solve research oriented tasks.

ECTS-Credit Points Module:



Written exam

Workload in Hours:

Independent Study Time: 124, Study Time in Lecture: 56

Course: High-Order FEM


Alexander Düster




Summer Semester


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


[1] Alexander Düster, High-Order FEM, Lecture Notes, Technische Universität Hamburg-Harburg, 164 pages, 2014
[2] Barna Szabo, Ivo Babuska, Introduction to Finite Element Analysis – Formulation, Verification and Validation, John Wiley & Sons, 2011

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