Abstract

A new mixed finite element approximation of Maxwell's problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the natural norm for this unknown. In particular, convergence also applies to singular solutions, for which classical nodal-based interpolations are known to suffer from spurious convergence upon mesh refinement.

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Published on 05/09/19

DOI: 10.1137/11083536
Licence: CC BY-NC-SA license

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