Magnetic liquids or ferrofluids are complex fluids. Some of their physical properties can be influenced by applying an outer magnetic field. One interesting phenomenon is the so-called Rosensweig instability where a magnetic field is applied normal to a flat an horizontal free surface. If the magnetic field strength exceeds a certain threshold a spontaneous surface deformation takes place. The interface between ferrofluid and air forms a regular hexagonal pattern of peaks.
This phenomenon can be described by a coupled systems of nonlinear partial differential equations involving the Young-Laplace equation on the free surface. A decoupling of the whole problem into two subproblems will be presented. Both are solved using finite element methods. For the Young-Laplace equation as one subproblem, a finite element error estimate will be proven.
Finally, numerical simulations of the Rosensweig instability using different discretisation schemes will be given.
