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Numerical Methods for Partial Differential Equations II - Single View

Basic Information
Type of Course Lecture Long text
Number 108411 Short text
Term SoSe 2022 Hours per week in term 4
Expected no. of participants Study Year
Max. participants
Credits Assignment enrollment
Hyperlink https://sso.uni-muenster.de/LearnWeb/learnweb2/course/view.php?id=59681
Language english
Dates/Times/Location Group: [no name] iCalendar export for Outlook
  Day Time Frequency Duration Room Room-
plan
Lecturer Status Remarks Cancelled on Max. participants
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Tue. 12:00 to 14:00 weekly 05.04.2022 to 05.07.2022  Einsteinstr. 64 - M B 6 (M 6)        
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Fri. 12:00 to 14:00 weekly 08.04.2022 to 08.07.2022  Einsteinstr. 64 - M B 6 (M 6)        
Group [no name]:
 


Responsible Instructor
Responsible Instructor Responsibilities
Rave, Stephan, Dr. responsible
Curriculae
Graduation - Curricula Sem ECTS Bereich Teilgebiet
Master - Mathematics (88 F23 20) -
Master - Mathematik (88 105 13) -
Master - Mathematik (88 105 10) -
Exams / Modules
Number of Exam Module
18004 Vorlesung 2 (mit Studienleistung) - Master Mathematik Version 2013
18001 Vorlesung 1 - Master Mathematik Version 2013
20001 Lecture 1 - Master Mathematics Version 2020
20003 Lecture 2 - Master Mathematics Version 2020
Assign to Departments
Fachbereich 10 Mathematik und Informatik
Contents
Description

Many processes in science and engineering are governed by conservation laws. These conservation laws state that the temporal change of a conserved quantity in a given volume is equal to the integral of the flux of this quantity across the volume's boundary. When the flux is a function of the conserved quantities, these conservation laws lead to a system of first-order partial differential equations. Some examples among many others are the Euler equations in fluid dynamics or the modelling of traffic flow.

In this lecture we will be concerned with the analysis and numerical approximation of first-order partial differential equations arising from conservation laws. In particular we will study so-called Finite Volume methods, which are based on a discrete formulation of the conservation laws on a finite set of control volumes covering the computational domain. In the accompanying exercises, in addition to deepening our theoretical knowledge, we will gain practical experience with the implementation of finite volume schemes using the Python programming language.

Literature
  • T. Barth und M. Ohlberger. Finite volume methods: foundation and analysis. In T.J.R. Hughes E. Stein, R. de Borst, editor, Encyclopedia of Computational Mechanics , volume 1, chapter 15. John Wiley & Sons, Ltd, 2004.
  • R. Eymard, T. Galluoët und R. Herbin. Finite volume methods. In Handbook of numerical analysis, Vol. VII , pages 713-1020. North-Holland, Amsterdam, 2000.
  • D. Kröner. Numerical schemes for conservation laws . Wiley-Teubner Series Advances in Numerical Mathematics. John Wiley & Sons Ltd., Chichester, 1997.
Prerequisites

Some familiarity with partial differential equations and their numerical approximation (e.g. Finite Element method for elliptic equations) is helpful but not required. Basic knowledge of the Python programming language is required to follow the programming exercises.


Structure Tree
Lecture not found in this Term. Lecture is in Term SoSe 2022 , Currentterm: WiSe 2022/23