A variational approach to compute singular axisymmetric electromagnetic fields

We propose a new variational approach to solve the axisymmetric Maxwell equations in singular domains, as for example in non convex polygonal domains. We focus on the computation of the electric field E = (E_r,E _z). We show that the key point is to solve axisymmetric Laplace-like operators in the singular domain. This can not be performed by a standard finite element method, which would give a solution identically equal to zero. To get the true non-vanishing solution, we decompose the computational domain into several subdomains, then we derive an ad hoc variational formulation, in which the interface conditions are imposed through a method deduced from a Nitsche approach. Numerical examples are shown.