Finite Elements for the Time Harmonic Maxwell’s Equations

We review the time harmonic Maxwell’s system and its approximation via the finite element method. The problem under consideration is strictly related to the so-called interior Maxwell’s eigenproblem.Standard nodal (Lagrangian) elements are known to provide useless results on general meshes. Special two-dimensional meshes have been shown to give good results, but the use of them is not recommended. The use of a penalty strategy with nodal elements has been proved to give wrong results for domains with singularities. Some special schemes, which make use of nodal elements, circumvent this problem; one of them is described in this paper.On the other hand the so-called edge elements represent the natural choice. A new proof of convergence for a method based on edge elements is summarized.