Miniworkshop
Miniworkshop "High Order Finite Elements" organized by Joachim Schöberl,
October 19, 2005, 10:15 - 16:00, Room: HF 136
Lectures on "High order FEM"
- Introduction
- Motivation
The finite element method-some basic principles
A simple one-dimensional example (with smooth/non-smooth solution) - Hierarchic shape functions
Hierarchic shape functions for one-dimensional problems
Hierarchic shape functions for quadrilaterals
Hierarchic shape functions for hexahedrals - Mapping functions
Mapping concepts
The blending function method
Exact representation of geometry vs. low order polynomial approximation
Quasi-regional mapping
Representation of rigid body modes
Distorted elements - Computation of element matrices, assembly, contraint enforcement and solution
Computation of element matrices
Assembly and contraint enforcement
Solution (static condensation) - Convergence characteristics
Classification
A priori estimates
The choice of finite element spaces
Error estimation in energy norm (by extrapolation)
A one-dimensional example
A two-dimensional example - Mechanical models and finite elements for thin-walled structures
Three-dimensional curved thin-walled structures
The Reissner-Mindlin plate theory
The locking phenomenon - Computation of thin-walled structures
Plate with columns
Scordelis-Lo shell
A hemispherical shell with stiffener
Literature
[1] Barna Szabo, Ivo Babuska.
Finite Element Analysis,
John Wiley & Sons, 1991.
[2] Barna Szabo, Alexander Düster, Ernst Rank.
The p-version of the Finite Element Method,
Encyclopedia of Computational Mechanics,
John Wiley & Sons, 2004.
[3] Alexander Düster.
High order FEM,
Lecture Notes (will be available),
TU München, 2005.
The lecture was held for students of the International Master Program in Computational Mechancis as well as for students of Civil Engineering at the Technische Universität München for the first time during summer term 2005. Lecture notes will be available. Please visit also the corresponding homepage for additional information and material (slides, maple worksheets and C++ code).
The program as PDF
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