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# 317.016 Fundamentals of Finite Element Methods This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2023W 2022W 2021W 2020W 2019W 2018W 2017W 2016W 2015W 2014W 2013W 2012W 2011W 2011S 2010S 2009S 2008S 2007S 2006S 2005S 2004S 2003S

2023W, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• Format: Hybrid

## Learning outcomes

After successful completion of the course, students are able to...

• ... state and describe the components of modeling and numerical analysis, and analyze and categorize model equations with respect to their properties.
• ... explain the concept of a vector space and related topics such as scalar product, norm, basis, or discrete subspaces and give relevant examples.
• ... define and use the concept of the weak derivative.

• ... determine and analyze a corresponding weak form for a given partial differential equation, name types of boundary conditions, and evaluate and use given boundary conditions.
• ... describe and analyze aspects of polynomial interpolation relevant to the FEM.

• ... explain and apply the Galerkin FEM using the isoparametric principle, i.e. formulate expressions for the geometric representation of the computational domain or for the searched function using interpolation polynomials.
• ... calculate integrals from the FEM, if necessary by means of numerical integration, and select suitable methods as well as state, explain, and apply the concept of the reference element and examples thereof.
• ... illustrate and carry out the assembly process and evaluate properties of the system of linear equations produced in the FEM.

• ... explain the application of FEM to problems in structural or fluid mechanics and state their associated properties.
• ... state and illustrate the properties and procedures of the computational grids used in FEM.
• ... discuss and evaluate aspects of the (error) analysis of numerical methods.
• ... classify and apply time discretization methods.
• ... distinguish the collocation method from Galerkin-FEM.

## Subject of course

The participants will be guided towards independently discretizing and solving a given partial differential equation. In particular, topics such as choice of basis functions, boundary conditions, and solution methods are essential to the course. The mathematical foundation is touched upon. The lecture is oriented towards partial differential equations relevant in engineering (e.g., solid mechanics or fluid mechanics). Common mistakes when using numerical methods are discussed.

## Teaching methods

Online lecture with power point presentation, derivation of equations, explaining sketches and figures; discussion of case studies

## Mode of examination

Written

This course will be delivered in German language!

## Course dates

DayTimeDateLocationDescription
Tue11:00 - 14:0003.10.2023 - 23.01.2024HS 18 Czuber - MB Fundamentals Finite Element Methods
Fundamentals of Finite Element Methods - Single appointments
DayDateTimeLocationDescription
Tue03.10.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue10.10.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue17.10.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue24.10.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue31.10.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue07.11.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue14.11.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue21.11.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue28.11.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue05.12.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue12.12.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue19.12.202311:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue09.01.202411:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue16.01.202411:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods
Tue23.01.202411:00 - 14:00HS 18 Czuber - MB Fundamentals Finite Element Methods

## Examination modalities

All exams are in German language only. Thus, please refer to the information in the German version of this page.

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Fri16:00 - 18:0018.10.2024FH Hörsaal 1 - MWB written17.09.2024 09:00 - 17.10.2024 17:00TISSAnfang WS 2024/2025
Fri14:00 - 16:0013.12.2024FH Hörsaal 1 - MWB written11.11.2024 09:00 - 12.12.2024 17:00TISSMitte WS 2024/2025
Wed15:00 - 17:0022.01.2025Informatikhörsaal - ARCH-INF written15.12.2024 09:00 - 21.01.2025 17:00TISSEnde WS 2024/2025
Wed14:00 - 16:0019.03.2025FH Hörsaal 1 - MWB written17.02.2025 09:00 - 18.03.2025 17:00TISSAnfang SS 2025
Fri11:00 - 13:0016.05.2025HS 18 Czuber - MB written16.04.2025 09:00 - 15.05.2025 17:00TISSMitte SS 2025
Wed14:00 - 16:0018.06.2025FH Hörsaal 1 - MWB written17.05.2025 09:00 - 17.06.2025 17:00TISSEnde SS 2025

## Course registration

Begin End Deregistration end
03.09.2023 08:00 28.03.2024 22:59 28.03.2024 22:59

## Group Registration

GroupRegistration FromTo
SK03.08.2023 08:0008.06.2024 23:59

## Curricula

Study CodeObligationSemesterPrecon.Info
033 245 Mechanical Engineering Mandatory5. Semester
Course requires the completion of the introductory and orientation phase
033 282 Mechanical Engineering - Management Mandatory
Course requires the completion of the introductory and orientation phase
066 473 Chemical and Process Engineering for Sustainable Production Mandatory elective
066 482 Mechanical Engineering - Management Not specified
Course requires the completion of the introductory and orientation phase
734 Apparatus, Plant and Process Engineering Mandatory8. Semester
735 Chemical Engineering Mandatory8. Semester

## Literature

K.-J. Bathe: Finite Elemente Methoden, Springer Verlag, 1986;

Zienkiewicz, Taylor: The Finite Element Method, Fourth Edition, Mc Graw Hill, 1989; T.J.R.

Hughes: The Finite Element Method, Prentice Hall, 1987

## Previous knowledge

Knowledge in mechanics and linear algebra

German