  This paper develops $P^K$-based non-central and central Runge-Kutta
discontinuous Galerkin (DG) methods with WENO limiter for the one- and
two-dimensional special relativistic magnetohydrodynamical (RMHD) equations,
$K=1,2,3$. The non-central DG methods are locally divergence-free, while the
central DG are "exactly" divergence-free but have to find two approximate
solutions defined on mutually dual meshes. The adaptive WENO limiter first
identifies the "troubled" cells by using a modified TVB minmod function, and
then uses the WENO technique to locally reconstruct a new polynomial of degree
$(2K+1)$ inside the "troubled" cells replacing the DG solution by based on the
cell average values of the DG solutions in the neighboring cells as well as the
original cell averages of the "troubled" cells. The WENO limiting procedure
does not destroy the locally or "exactly" divergence-free property of magnetic
field and is only employed for finite "troubled" cells so that the
computational cost can be as little as possible. Several test problems in one
and two dimensions are solved by using our non-central and central Runge-Kutta
DG methods with WENO limiter. The numerical results demonstrate that our
methods are stable, accurate, and robust in resolving complex wave structures.
