  A moving mesh discontinuous Galerkin method is presented for the numerical
solution of hyperbolic conservation laws. The method is a combination of the
discontinuous Galerkin method and the mesh movement strategy which is based on
the moving mesh partial differential equation approach and moves the mesh
continuously in time and orderly in space. It discretizes hyperbolic
conservation laws on moving meshes in the quasi-Lagrangian fashion with which
the mesh movement is treated continuously and no interpolation is needed for
physical variables from the old mesh to the new one. Two convection terms are
induced by the mesh movement and their discretization is incorporated naturally
in the DG formulation. Numerical results for a selection of one- and
two-dimensional scalar and system conservation laws are presented. It is shown
that the moving mesh DG method achieves the theoretically predicted order of
convergence for problems with smooth solutions and is able to capture shocks
and concentrate mesh points in non-smooth regions. Its advantage over uniform
meshes and its insensitiveness to mesh smoothness are also demonstrated.
