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.
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