Numerical Analysis Group

Finite Element Methods

Finite element methods, Winter 2015/16

Current announcements

  • The schedule for the oral exams on Thursday and Friday this week can now be downloaded in the Exam section. Please make sure to arrive early enough in order to allow smooth examinations.
  • The dates for the oral examinations on March 31 and April 1 can be found here. The precise schedule will be available on March 29.
  • There will be a second Q&A-session at March 23, 9:45 - 11:00 at room 3.061. Please prepare topics and questions, for there will be no input from our side.
  • The schedule for the oral exams at Wednesday 17.2.2016 can now be downloaded in the Exam section. Please make sure to arrive early enough in order to allow smooth examinations.
  • Small corrections of the lecture notes.
  • A complete version of the lecture notes is now available. It includes a corrected estimate of the computational costs for the nested iteration.
  • We added two questions about the Discontinuous Galerkin chapter. In the exams these new questions will be contained in the category of the eigenvalue Chapter.
  • Lecture notes updated up to Section 5.4.
  • The first part of Chapter 5 is now online.
  • The questions for the oral examination have been updated (questions for Chapter 4 included).
  • The last problem sheet can now be found in the download section.
  • There is an update of the questionary which contains the questions to the multigrid chapter and a shortend list of questions for Chapter 1.
  • Problem sheet 12 is now available.
  • The lecture notes were complemented by a large part of the following chapter about elliptic eigenvalue problems.
  • We decided that lecture notes on the multigrid and following chapters will only be provided in English.
  • Small corrections at the multigrid chapter.
  • Problem sheet 10 is available.
  • The english lecture notes now contain the complete multigrid chapter.
  • Correction on Problem sheet 8: false hint in Problem 29 part b).
  • Problem sheet 9 is now available. Please remember that the problem class in the week of christmas takes place on 21st Monday at 14:00 in SR 1.067.
  • The registration for the oral examinations is now open:
    https://campus.studium.kit.edu/english/exams/registration.php
    We offer two dates which are February 17 and March 31.
    For more information visit the Exam section.
  • Section 3.6 was added to the lecture notes.
  • The problem class in the week of christmas is on 21st Monday at 14:00 in SR 1.067.
  • Problem sheet 8 is now available.
  • Section 3.3-3.5 are now contained in the lecture notes.
  • The list of question for the exams can now be downloaded in the Exam section. Only the questions for Chapter 1 and 2 are available. The rest of the questions will be provided after the corresponding Chapters were discussed in the lecture.
  • Update of lecture notes.
  • Problem sheet 7 is now available.
  • Correction on Problem sheet 6. The conjecture of part (b) was wrong.
  • For the oral examinations we offer two dates: February 17 and March 31, 2016. The link for registering for the examinations will follow.
  • The complete second chapter of the lecture notes is now available.
  • Problem sheet 6 is now available.
  • Update of lecture notes with more detailed density arguments.
  • Update of lecture notes.
  • Problem sheet 5 is now available.
  • Update of lecture notes.
  • The lecture notes were updatet and the german version now contains the next chapter.
  • There was an update of the german lecture notes.
  • Problem sheet 4 is now available.
  • The complete first chapter of the lecture notes is now online.
  • A corrected version of Problem sheet 3 is available. There was a typo in the assumptions in Problem 9 part b).
  • The lecture notes were updated and problem sheet 3 can now be downloaded.
  • The lecture notes were updated and problem sheet 2 can now be downloaded.
  • The first problem sheet is now available.
  • A german version of the lecture notes can now be found in the supplementary materials.
  • From now on, the lectures on Tuesday will be in room -1.013.
  • Uploaded first sections of the lecture notes
  • In order to avoid frequent replacements due to obligations of Prof. Hochbruck for the DFG, there is an alternative date for lectures on mondays 9:45 in room 3.069. The lecture dates are always announced here.

Persons

Weekly hours

4 SWS lecture + 2 SWS problem class

Contents and Prerequisites

This lecture provides an introduction to the theory of finite element methods for elliptic boundary value problems in dimension one and two. In particular, stability and convergence will be proved and concepts for the implementation of such methods will be explained. Moreover, the numerical solution of elliptic eigenvalue problems and mixed methods for saddle point problems will be investigated.

The students are expected to be familiar with the basics of numerical analysis, in particular interpolation, numerical integration, solution of linear systems and eigenvalue problems. 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, 9:45-11:15 in SR 3.069, building 20.30 (alternative date)
Tuesday, 9:45-11:15 in SR -1.013, building 20.30
Thursday, 14:00-15:30 in SR 1.066/1.067, 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 43: Tuesday 20.10. and Thursday 22.10.
cw 44: Tuesday 27.10. and Thursday 29.10.
cw 45: Monday 02.11. and Tuesday 03.11.
cw 46: Tuesday 10.11. and Thursday 12.11.
cw 47: Tuesday 17.11. and Thursday 19.11.
cw 48: Tuesday 24.11. and Thursday 26.11.
cw 49: Tuesday 01.12. and Thursday 03.12.
cw 50: Monday 07.12. and Tuesday 08.12.
cw 51: Tuesday 15.12. and Thursday 17.12. in Room 2.059
cw 52: Tuesday 22.12.
cw 01:       Thursday 07.01.
cw 02: Tuesday 12.01 and Thursday 14.01.
cw 03: Tuesday 19.01 and Thursday 21.01.
cw 04: Monday 25.01. and Tuesday 26.01.
cw 05: Wednesday 03.02. and Thursday 04.02. (problem class on Tuesday)
cw 06: Monday 08.02. and Tuesday 09.02.

Exam

We offer two dates for the oral examinations which are February 17 and March 31.

The registration for the oral examinations is now open under https://campus.studium.kit.edu/english/exams/registration.php. Registration is open until February 10 / March 24 and you can resign until February 14 / March 28.

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 Chapter 1-5

Schedule for the exams on Wednesday, February 17.
Schedule for the exams on Thursday March 31 and Friday April 1.

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.

Supplementary material

The german lecture notes include the chapters from previous lectures and will also be updated as the lecture progresses. There maybe slight differences between the english and the german version.

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

Literature