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 epsilon = upsilon/c where upsilon is the characteristic velocity associated with the physical problem an d c is the speed of light. This enables us to derive the quasistatic a nd 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.