Unfitted discretization methods for PDEs on embedded manifolds and coupled manifold-bulk problems
Andre Massing (Umeå University, Sweden)
Mat Larson (Umeå University, Sweden)
Luca Formaggia (Politecnico di Milano, Italy)
Many advanced engineering and modeling problems involve coupled physics both on lower-dimensional manifold-like geometries and its embedding bulk domain.
Important examples include flow in porous or poroelastic media with cracks or channel networks, fluid-structure interaction involving thin membranes and shells, and transport of surfactants on evolving surfaces coupled to bulk domains.
There is currently a rapid development of numerical methods for efficient computational solution of such problems. A basic challenge is to construct efficient methods for representation of the complex or evolving geometry of the domain. Several different approaches are considered including methods utilizing a standard mesh, extended finite element methods, cut finite element methods, and immersed methods.
In this minisymposium we present recent developments in this area with a particular focus on novel extended and cut finite element methods.
