Research
research projects.
I am currently working on two projects
Finite element discretization of Yang–Mills connections on non-trivial bundles.
This project develops finite element methods for Yang-Mills connections on principal bundles. The discretization is based on local connection forms and uses discontinuous finite elements, with compatibility conditions imposed across edges. In the abelian case this leads to a linear saddle-point finite element problem, and the method is tested on the Hopf fibration as a model non-trivial bundle. This is joint work with my supervisors Geir Bogfjellmo and Charles Curry. A preprint will be available on arxiv.
Zeitlin model with boundary conditions.
Together with Klas Modin, I study a Zeitlin-type finite-dimensional model for the two-dimensional Euler equations with boundary constraints. The idea is to represent domain boundaries through level-set constraints for the stream function, avoiding a direct restriction of the continuous problem to the boundary. The resulting model gives a structure-preserving way to approximate Euler dynamics on domains with boundaries, and is implemented with the Quflow library.