Discrete boundary finite element schemes for an exterior problem for the time-harmonic Maxwell's equation

A general boundary integral formulation using Galerkin procedure is applied to compute the scattering electric field produced by the diffraction of an incident electromagnetic wave by a perfectly conducting obstacle. This electric field satisfies the three-dimensional time-harmonic Maxwell's equations for which the skin currents and charges are to be approximated using boundary finite element method. With the help of linear and quadratic finite elements of Lagrange type, we introduce an approximate surface on which the discrete formulation is defined, and construct approximate surface currents and charges. In addition, we study the existence and the uniqueness of the solution of the discrete problem and develop some error estimates for the currents and charges. Numerical results are also presented in order to validate our numerical approach.