  We develop a high order accurate numerical method for solving the elastic
wave equation in second-order form. We hybridize the computationally efficient
Cartesian grid formulation of finite differences with geometrically flexible
discontinuous Galerkin methods on unstructured grids by a penalty based
technique. At the interface between the two methods, we construct projection
operators for the pointwise finite difference solutions and discontinuous
Galerkin solutions based on piecewise polynomials. In addition, we optimize the
projection operators for both accuracy and spectrum. We prove that the overall
discretization conserves a discrete energy, and verify optimal convergence in
numerical experiments.
