Well posedness and finite element approximability of two-dimensional time-harmonic electromagnetic problems involving non-conducting moving objects with stationary boundaries

Brignone, Massimo; Raffetto, Mirco

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 1157-1192.

A set of sufficient conditions for the well-posedness and the convergence of the finite element approximation of two-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting moving objects with stationary boundaries is provided for the first time to the best of authors’s knowledge. The set splits into two parts. The first of these is made up of traditional conditions, which are not restrictive for practical applications and define the usual requirements for the domain, its boundary, its subdomains and their boundaries, the boundary conditions and the constitutive parameters. The second part consists of conditions which are specific for the problems at hand. In particular, these conditions are expressed in terms of the constitutive parameters of the media involved and of the velocity field. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve axially moving media.

Classification : 65N30, 65N12, 35Q60
Mots clés : Electromagnetic scattering, time-harmonic electromagnetic fields, bianisotropic media, moving media, variational formulation, well posedness, finite element method, convergence of the approximation

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