Special Radon Semester on Computational Mechanics
Linz, October-December 2005
"hp-techniques in mechanics" organized by Alexander Düster


Miniworkshop "High Order Finite Elements" organized by Joachim Schöberl,
October 19, 2005, 10:15 - 16:00, Room: HF 136

Lectures on "High order FEM"

  1. Introduction

  2. Motivation
    The finite element method-some basic principles
    A simple one-dimensional example (with smooth/non-smooth solution)

  3. Hierarchic shape functions
    Hierarchic shape functions for one-dimensional problems
    Hierarchic shape functions for quadrilaterals
    Hierarchic shape functions for hexahedrals

  4. 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

  5. Computation of element matrices, assembly, contraint enforcement and solution
    Computation of element matrices
    Assembly and contraint enforcement
    Solution (static condensation)

  6. Convergence characteristics
    A priori estimates
    The choice of finite element spaces
    Error estimation in energy norm (by extrapolation)
    A one-dimensional example
    A two-dimensional example

  7. Mechanical models and finite elements for thin-walled structures
    Three-dimensional curved thin-walled structures
    The Reissner-Mindlin plate theory
    The locking phenomenon

  8. Computation of thin-walled structures
    Plate with columns
    Scordelis-Lo shell
    A hemispherical shell with stiffener


[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 M√ľnchen, 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 Universit√§t 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

URL: www.ricam.oeaw.ac.at/specsem/sscm/structure/lectures/duester.php

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