# Current announcements

- On
**Monday, August 6, at 11:00**we will have a**Q&A-session**about the lecture in room 3.060. Please prepare questions. - The lecture notes were updated.
- Problem sheet 14 is now available. It will be discussed on Tuesday, July 17.
- Update of the lecture notes.
- On
**Monday, July 16,**there will be a**repetition class**instead of the lecture. - The questions for the exams are available here and the registration for the exam is now open (Number of exam 7700046, German title "Numerische Methoden für zeitabhängige partielle Differentialgleichungen", English title "Numerical Methods for Time-Dependent Partial Differential Equations"). The exams take place between August 6 and 17.
- The solution to problem 37 is available here.
- Problem sheet 13 is now available. It will be discussed on Tuesday, July 10.
- Show old announcements

# Persons

- Prof. Dr. Marlis Hochbruck (lectures)
- M.Sc. Constantin Carle (problem classes)
- M.Sc. Jan Leibold (problem classes)

# Weekly hours

4 SWS lecture + 2 SWS problem class

# Contents and Prerequisites

The aim of this lecture is to construct, analyze and discuss the efficient implementation of numerical methods for time-dependent partial differential equations (pdes). We will consider traditional methods and techniques as well as very recent research.

The students are expected to be familiar with the basics of the numerical analysis of the time integration of ordinary differential equations (Runge-Kutta and multistep methods) and of finite element methods for elliptic boundary element methods. The lecture starts with a review on Runge-Kutta and multistep methods. Some basic knowledge in functional analysis and the analysis of boundary value problem is helpful but the main results will be repeated in the lecture.

# Schedule

## Lectures

Monday, | 15:45-17:15 in SR 3.061, building 20.30 |

Tuesday, | 17:30-19:00 in SR 3.061, building 20.30 (alternative date) |

Friday, | 9:45-11:15 in SR 3.061, building 20.30 |

## Problem classes

Tuesday, | 15:45-17:15 in SR 2.066, building 20.30 |

## Weekly schedule

Please note that the dates for the lectures and problem classes may vary from week to week. The dates for the next weeks are listed below. If changes to already announced dates are required they will be highlighted by color.

cw 16: | Mo | 16.4. | (lecture), | Tu | 16.4., 15:45 | (tutorial), | Fr | 20.4. | (lecture) |

cw 17: | Mo | 23.4. | (lecture), | Tu | 24.4., 15:45 | (tutorial), | Fr | 27.4. | (lecture) |

cw 18: | Mo | 30.4. | (lecture), | Fr | 04.5. | (tutorial) | |||

cw 19: | Mo | 07.5. | (lecture), | Tu | 08.5., 15:45 | (tutorial), | Fr | 11.5. | (lecture) |

cw 20: | Mo | 14.5. | (lecture), | Tu | 15.5., 15:45 | (tutorial), | Fr | 18.5. | (lecture) |

cw 21: | Tu | 22.5., 15:45 | (tutorial), | Tu | 22.5., 17:30 | (lecture), | Fr | 25.5. | (lecture) |

cw 22: | Mo | 28.5. | (lecture), | Tu | 29.5., 15:45 | (tutorial), | Fr | 01.6. | (lecture) |

cw 23: | Tu | 05.6., 15:45 | (tutorial), | Tu | 05.6., 17:30 | (lecture), | Fr | 08.6. | (lecture) |

cw 24: | Mo | 11.6. | (lecture), | Tu | 12.6., 15:45 | (tutorial), | Tu | 12.6., 17:30 | (lecture) |

cw 25: | Mo | 18.6. | (lecture), | Tu | 19.6., 15:45 | (tutorial), | Tu | 19.6., 17:30 | (lecture) |

cw 26: | Mo | 25.6. | (lecture), | Tu | 26.6., 15:45 | (tutorial), | Fr | 29.6. | (lecture) |

cw 27: | Mo | 02.7. | (lecture), | Tu | 03.7., 15:45 | (tutorial), | Fr | 06.7. | (lecture) |

cw 28: | Mo | 09.7. | (lecture), | Tu | 10.7., 15:45 | (tutorial), | Tu | 10.7., 17:30 | (lecture) |

cw 29: | Mo | 16.7. | (repetition), | Tu | 17.7., 15:45 | (tutorial), | Fr | 20.7. | (lecture) |

# Exam

The registration for the exam is open (Number of exam 7700046, German title "Numerische Methoden für zeitabhängige partielle Differentialgleichungen", English title "Numerical Methods for Time-Dependent Partial Differential Equations"). The exams take place between August 6 and 17.

The format of the exams will be the following:

- Until the end of the semester, we will provide you with a list of possible questions for each chapter of the lecture.
- You randomly draw three questions from this list, each from another chapter. One question can be redrawn from the same chapter with the possibility to answer the original question.
- Then you are given 20 minutes for preparation (without any aid). Any notes that you prepare during this time can be used in the oral exam.
- The actual oral exam will last additional 20 minutes during which you have to answer the questions. This leaves approximatly 7 minutes for each question. If the answer is too short we expect you to present further details of the topic. In order to assure that you understand all aspects of the topic in question, you can always be asked further questions.
- The final grade will be the mean of the grades (1-6) from the three answered questions.

The list of questions can be found here: Questions

# Lecture notes (draft version)

The lecture notes provided here are a draft version, since they are written when the lecture progresses. This includes corrections shortly after the corresponding topic was discussed.

I am gratefull for any suggested corrections and improvements.

- lecture notes (version from 12.07.2018)

The lecture notes are a continuation of the lecture notes for the Finite Element Methods from WS 15/16.

# Problem sheets

sheet 1, sheet 2, sheet 3, sheet 4, sheet 5, sheet 6, sheet 7, sheet 8, sheet 9, sheet 10, sheet 11, sheet 12, sheet 13, sheet 14

Additional material:

- solution to problem 3
- files for problem 15 (updated)
- solution to problem 15
- sketch of solution to problem 18
- sketch of solution to problem 20
- files for problem 29 (updated)
- solution to problem 29
- Gronwall_DixonMcKee
- solution to problem 33
- solution to problem 37

# Literature

- M. Hochbruck, lecture notes
- M. Hochbruck, lecture notes "Numerik I, Numerik II & Numerische Methoden für Differentialgleichungen"
- S. Brenner, R. Scott, The Mathematical Theory of Finite Element Methods, Springer Texts in Appl. Mathematics, Vol 15, Springer-Verlag, 3rd ed., 2008
- D. Braess, Finite Elements, Cambridge University Press, 3rd ed., 2007