A hierarchy of approximate models for the Maxwell equations

In this paper we perform an asymptotic study of the Maxwell equations with respect to the small parameter ε = v/c where v is the characteristic velocity associated with the physical problem and c is the speed of light. This enables us to derive the quasistatic and Darwin models as respectively first and second order approximations of the Maxwell equations. Moreover, an interpretation of the obtained variational formulations gives us the appropriate boundary conditions for these models.