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We consider the numerical approximation of Maxwell's equations in time domainby a second order $H(curl)$ conforming finite element approximation. In orderto enable the efficient application of explicit time stepping schemes, weutilize a mass-lumping strategy resulting from numerical integration inconjunction with the finite element spaces introduced by Elmkies and Joly. Weprove that this method is second order accurate if the true solution isdivergence free, but the order of accuracy reduces to one in the general case.We then propose a modification of the finite element space, which yields secondorder accuracy in the general case.

A second order finite element method with mass lumping for Maxwell's equations on tetrahedra