Abstract
Scattering problems in electromagnetism imply the approximate computation of vector-valued fields. To do this with finite elements which were originally designed for scalar-fields, that is, nodal elements, is not correct, for such vectorial finite elements have serious drawbacks. They impose on fields which they are meant to approximate (electric field e and magnetic field h) a continuity of all components across inter-element boundaries which is not a necessary property of the fields. Simplicial finite elements, and more especially edge-elements, a brand of vector finite elements with degrees of freedom associated with the edges of the mesh are, as shown here, free of such drawbacks. First used in connection with eddy-current problems, they are shown to fit the scattering problem just as well, with no penalty in terms of computational time and with the expected additional advantage of not generating spurious modes when applied to the problem of the eigenmodes of resonating cavities.
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