Mur-nédélec finite element schemes for Maxwellʹs equations Original Research Article

We study mapped mass-lumped edge elements for approximating a three-dimensional scattering problem. The elements are mapped Mur-Nédélec second kind elements and the scheme is designed to handle anisotropic, inhomogeneous scatterers with moderately complicated geometry. A novel aspect of the scheme is the use of an unusual choice of the magnetic field finite element that results in a very efficient discrete curl operator. Using a non-standard dispersion analysis, we show that the phase accuracy of the cubic edge element does not deteriorate disastrously when the mesh is deformed. Our numerical experiments (in two dimensions) confirm that the scheme performs well on a distorted mesh and that it is efficient compared to the standard Yee scheme.