## Lecture Numerical Homogenisation (SS 2024)

Jun.-Prof. Dr. Mira Schedensack

Universität Leipzig

Fakultät für Mathematik und Informatik

Mathematisches Institut

#### Prerequisites:

Basic knowledge of functional analysis (Sobolev spaces,
weak formulations of partial differential equations, weak convergence)
is desirable. If necessary, this can be briefly repeated in the lecture.
Previous knowledge of computational partial differential equations
is helpful, but not necessary.
#### Content:

This lecture is devoted to numerical methods for multiscale problems.
These are partial differential equations (PDEs), where the coefficient of the
PDE can vary on a fine scale.
This lecture will discuss two numerical methods for these kind
of problems.
The first one is the
*Heterogeneous Multiscale Method* in the context of periodic
coefficients that is based on homogenisation results from analysis.
The second one is the
*Localized Orthogonal Decomposition Method*.
#### Lecture times:

The lecture will take place on Mondays from 9:15 to 10:45 in P701.
The first lecture will be on 8th April 2024.
#### Materials

##### Script

Script
##### Code

standard FEM with coefficient