# Current announcements

- 2017-07-19: Lecture notes updated.
- 2017-07-18: Added exercise sheet 7.
- 2017-07-11: Lecture notes updated.
- Show old announcements.

# People

Lectures and exercises will be given by Dr. Dietmar Gallistl and Dr. Christian Stohrer .# Language

In principal in german, upon request the course will be held in english.# Prerequisutes

The course is meant for Master students who are familiar with the basics of finite element methods and numerical methods for differential equations. Some knowledge on functional analysis is helpful.# Content and qualification objectives

The topic of the lecture are numerical multiscale methods presented exemplarily for elliptic problems.Students know the basic analytical results for existence and uniqueness of the solution of multiscale problems and from homogenization theory. In addition, they know methods for the numerical approximation of multiscale and the homogenized solution. They are able to analyze the convergence of these methods and asses the pros and cons of the different approaches.

The following four chapters are planned:

- Motivation
- Analytical fundamentals (basic results from analysis for elliptic partial differential equations and from homogenization theory)
- Approximation of the homogenized solution - Heterogeneous Multiscale Method
- Approximation of the multiscale solution - Local Orthogonal Decomposition

# Schedule

## Weekly hours

3h lecture and 1h problem class (6 credit points)## Lectures and problem classes

Monday, | 11:30-13:00 in SR 3.061, buildung 20.30 |

Tuesday, | 11:30-13:00 On the following three dates the lecture or problem classes will take place in SR 3.060: 2017-05-30, 2017-06-27, and 2017-07-25. |

Exercise 1: Tuesday, May 2, 2017 |

Exercise 2: Monday, May 22, 2017 |

Exercise 3: Tuesday, May 30, 2017 |

Exercise 4: Tuesday, June 13, 2017 |

Exercise 5: Tuesday, June 27, 2017 |

Exercise 6: Monday, July 10, 2017 |

Exercise 7: Tuesday, July 25, 2017 |

# Lectures material

## Lectures notes

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.We are grateful for any suggested corrections and improvements.

## Exercise sheets

- Sheet 1, Solution, Solution of programming exercise
- Sheet 2, Solution, Solution of programming exercise
- Sheet 3, Solution, Solution of programming exercise
- Sheet 4, Solution, Solution of programming exercise 4, Solution of programming exercise 5
- Sheet 5.
- Sheet 6, Solution (Exercise 22),
- Sheet 7,