Approximate models for the Maxwell equations

Starting from a variational formulation of Maxwell's equations with perfectly conducting and Silver-Muller boundary conditions, we set an abstract framework in which to perform an asymptotic analysis with respect to a small parameter v/c where v is a characteristic speed of the considered physics problem and c the speed of light. We then derive a variational formulation for the first and second order approximate models. We here partic ularly emphasize the second order model which is known as the Darwin model and thanks to an interpretion of the variational formulation, give Me correct boundary conditions for this problem.