  Consider the scattering of a time-harmonic electromagnetic plane wave by an
open cavity which is embedded in a perfectly electrically conducting infinite
ground plane. This paper concerns the numerical solutions of the open cavity
scattering problems in both transverse magnetic and transverse electric
polarizations. Based on the Dirichlet-to-Neumann (DtN) map for each
polarization, a transparent boundary condition is imposed to reduce the
scattering problem equivalently into a boundary value problem in a bounded
domain. An a posteriori error estimate based adaptive finite element DtN method
is proposed. The estimate consists of the finite element approximation error
and the truncation error of the DtN operator, which is shown to decay
exponentially with respect to the truncation parameter. Numerical experiments
are presented for both polarizations to illustrate the competitive behavior of
the adaptive method.
