Speaker:
Christophe Lehrenfeld, University of Göttingen
Abstract
Many simulation problems involve complex, evolving geometries with strong deformations and topology changes. Traditional finite element methods (FEM) use fitted meshes that conform to the geometry, but these can be difficult to generate and update. Geometrically unfitted FEM offer an alternative by separating the mesh from the geometry description. A basis discretization is defined on a simple background mesh and then adapted to the given geometry, enabling efficient handling of complex, time-dependent domains without costly remeshing.
Although unfitted or cut-cell methods provide great flexibility, they introduce several challenges. One specific challenge addressed in this talk is time integration. To obtain stable and accurate time integration we discuss several possible strategies and focus on two strategies: an extension-based generalization of the method-of-lines approach and unfitted space-time FEM formulations. We present the methods, discuss implementation details, provide a priori error estimates, and show numerical results.