APPROXIMATE MODELS FOR THE MAXWELL EQUATIONS

Starting from a variational formulation of Maxwell's equations with pe rfectly conducting and Silver-Muller boundary conditions, we set an ab stract framework in which to perform an asymptotic analysis with respe ct to a small parameter v/c where v is a characteristic speed of the c onsidered physics problem and c the speed of light. We then derive a v ariational formulation for the first and second order approximate mode ls. We here partic ularly emphasize the second order model which is kn own as the Darwin model and thanks to an interpretion of the variation al formulation, give Me correct boundary conditions for this problem.