Abstract:
Finite Element Methods have found prominent use in applications involving electromagnetism. In this talk we will go through an introduction to non-Abelian gauge theories to formulate a generalization of Maxwell's equations and continuity equations in this setting. Based on differential geometric concepts of connections and parallel transport as well as numerical relativity, we will touch upon parts of a work-in-progress FEM discretization which holds the potential to intrinsically reflect gauge symmetry and charge conservation.