# Two-level finite element discretizations for simulating Bose-Einstein condensates

**Patrick Henning
**

Numerical Analysis Group

Department of Mathematics

KTH

Stockholm

### Abstract:

In this talk we present a two-level discretization strategy for solving nonlinear Schrödinger equations. The scheme is based on finite element discretizations on two different scales of numerical resolution and involves the construction of a low-dimensional (coarse) generalized finite element space that exhibits high approximation properties. After giving a general introduction into the method, we present an application in quantum physics, namely the computation of ground states of so called Bose-Einstein condensates. Such condensates are ultra-cold gases which exhibit remarkable properties such as superfluidity (i.e. a frictionless flow). In the final part of the talk we will give an outlook on discretizations for simulating the dynamics of rotating condensates.