Nitsche type method for approximating boundary conditions in the static Maxwell equations

We propose a new method for handling boundary conditions in the Maxwell equations. This formulation is derived from a continuous finite element approach, supplemented with a Nitsche type method. Several years ago, the Nitsche method was introduced to impose weakly essential boundary conditions in the scalar Laplace operator. Then, it has been worked out more generally and transferred to continuity conditions. We propose here an extension to the vector div -curl problem, especially to the Maxwell equations. Compared with the penalty method, this approach has the advantage to be consistent with the original equations. We formulate the method and report some numerical experiments.