Karl Olav Tyssvang

I am a postgraduate student at the Mathematical Institute, University of Oxford, where I am currently undertaking my PhD as part of the ERC project GeoFEM (Geometric Finite Elements). My advisors are Prof. Kaibo Hu, and Prof. Snorre H. Christiansen.

My academic background is in differential geometry, functional analysis, and programming. I am curious about how we can represent geometries and partial differential equations on computers. To answer such questions it is crucial to understand the links between the fields of discrete differential geometry and finite element methods.

Numerical methods for partial differential equations tend to assume the prescence of a Euclidean metric. We can describe the same equations on more exciting geometries, and a lot of the analytic tools work regardless of the underlying metric. I believe studying discretizations in this general setting can inspire further developments of established methods.

Things you can read

Jan 2026	A presentation on differential forms, made for the Oxford FEM reading group.
Spring 2025	My master's thesis Non-Euclidean Elements.