  We propose and analyze a class of robust, uniformly high-order accurate
discontinuous Galerkin (DG) schemes for multidimensional relativistic
magnetohydrodynamics (RMHD) on general meshes. A distinct feature of the
schemes is their physical-constraint-preserving (PCP) property, i.e., they are
proven to preserve the subluminal constraint on the fluid velocity and the
positivity of density, pressure, and specific internal energy. Developing PCP
high-order schemes for RMHD is highly desirable but remains a challenging task,
especially in the multidimensional cases, due to the inherent strong
nonlinearity in the constraints and the effect of the magnetic divergence-free
condition. Inspired by some crucial observations at the PDE level, we construct
the provably PCP schemes by using the locally divergence-free DG schemes of the
recently proposed symmetrizable RMHD equations as the base schemes, a limiting
technique to enforce the PCP property of the DG solutions, and the
strong-stability-preserving methods for time discretization. We rigorously
prove the PCP property by using a novel "quasi-linearization" approach to
handle the highly nonlinear physical constraints, technical splitting to offset
the influence of divergence error, and sophisticated estimates to analyze the
beneficial effect of the additional source term in the symmetrizable RMHD
system. Several two-dimensional numerical examples are provided to confirm the
PCP property and to demonstrate the accuracy, effectiveness and robustness of
the proposed PCP schemes.
