# Current announcements

- The
**schedule for the oral exams**is now available and can be found here. - The
**Q&A-session**tomorrow is hold in a**different room: at 9:45 at room 3.061**. - The deadline for registering for the exams is
**September 11**. Note that university portal for students only lists the German name of the lecture, which is "Numerische Methoden für zeitabhängige PDGlen". The exams will be on**Friday, September 30**. The precise schedule will be available on Monday, September 26. - One week before the oral exams, on
**Wednesday September 21 at 9:45**in room 1.067, we will have our**traditional Q&A-session**about the lecture. Please prepare questions. - The full list of questions for the oral exam can now be found in the Exam section.
- A complete version of the lecture notes is now available for download.
- The last problem class on July 20 will be used to answer questions.
- Update of the lecture notes.
- Problem sheet 12 is now available.
- The questions for the exam about Chapters 6 and 7 are now available for download. The questions about the Chapter 8 will follow.
- The results of the evaluation of the lecture are ready and can be found here .
- There is an update for the lecture notes.
- Problem sheet 11 is now available.
- The lecture notes were updated.
- Show old announcements

# Persons

- Prof. Dr. Marlis Hochbruck (lectures)
- Dipl. math. techn. Simone Buchholz (problem classes)
- Dipl. math. techn. David Hipp (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 1.067, building 20.30 (alternative date) |

Tuesday, | 9:45-11:15 in SR 2.067, building 20.30 |

Thursday, | 9:45-11:15 in SR 1.067, building 20.30 |

## Problem classes

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

## Lecture dates

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: | Tuesday | 19.4. | and | Thursday | 21.4. |

cw 17: | Tuesday | 26.4. | and | Thursday | 28.4. |

cw 18: | Tuesday | 03.5. | and | Wednesday | 04.5. (problem classes on Monday 02.5.) |

cw 19: | Wednesday | 11.5. | and | Thursday | 12.5. (problem classes on Tuesday 10.5.) |

cw 20: | Tuesday | 17.5. | |||

cw 21: | Monday | 23.5. | and | Tuesday | 24.5. |

cw 22: | Tuesday | 31.5. | and | Thursday | 02.6. |

cw 23: | Tuesday | 07.6. | and | Thursday | 09.6. |

cw 24: | Tuesday | 14.6. | and | Thursday | 16.6. |

cw 25: | Monday | 20.6. | and | Thursday | 23.6. |

cw 26: | Wednesday | 29.6. | and | Thursday | 30.6. (problem classes on Tuesday 28.6.) |

cw 27: | Thursday | 07.7. | |||

cw 28: | Monday | 11.7. | and | Thursday | 14.7. |

cw 29: | Monday | 18.7. | and | Tuesday | 19.7. |

# Exam

The oral exams will take place on Friday, September 30.

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 19.7.2016)

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

Additional material:

- files for problem 12
- solution of problem 12
- files for problem 28
- Gronwall_DixonMcKee
- solution to Problem 30

# 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