A SECOND-ORDER FINITE ELEMENT METHOD WITH MASS LUMPING FOR MAXWELL'S EQUATIONS ON TETRAHEDRA

We consider the numerical approximation of Maxwell's equations in the time domain by a second-order H(curl) conforming finite element approximation. In order to enable the efficient application of explicit time-stepping schemes, we utilize a mass-lumping strategy resulting from numerical integration in conjunction with the finite element spaces introduced in [A. Elmkies and P. Joly, C. R. Acad. Sci. Paris Ser. I Math., 325 (1997), pp. 1217-1222]. We prove that this method is second-order accurate if the true solution is divergence 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 second-order accuracy in the general case.