  We formulate and validate a finite element approach to the propagation of a
slowly decaying electromagnetic wave, called surface plasmon-polariton, excited
along a conducting sheet, e.g., a single-layer graphene sheet, by an electric
Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's
equations, we derive a variational formulation that enables a direct numerical
treatment of the associated class of boundary value problems by appropriate
curl-conforming finite elements. The conducting sheet is modeled as an
idealized hypersurface with an effective electric conductivity. The requisite
weak discontinuity for the tangential magnetic field across the hypersurface
can be incorporated naturally into the variational formulation. We carry out
numerical simulations for an infinite sheet with constant isotropic
conductivity embedded in two spatial dimensions; and validate our numerics
against the closed-form exact solution obtained by the Fourier transform in the
tangential coordinate. Numerical aspects of our treatment such as an absorbing
perfectly matched layer, as well as local refinement and a-posteriori error
control are discussed.
