C01 Singularity formation in dissipative harmonic flows

In this project we study the harmonic map heat flow equation and some of its variants, e.g., the Landau-Lifshitz-Gilbert equation. In these equations singularities are known to appear generically and spontaneously. Guided by analytical theory, we shall develop a reliable and flexible numerical simulation environment to capture singular phenomena based on tailor- made finite element methods. In return, numerical simulations will allow us to attack open mathematical questions regarding the singularity formation of harmonic flows in two and three space dimensions.