  Weight-adjusted inner products are easily invertible approximations to
weighted $L^2$ inner products. These approximations can be paired with a
discontinuous Galerkin (DG) discretization to produce a time-domain method for
wave propagation which is low storage, energy stable, and high order accurate
for arbitrary heterogeneous media and curvilinear meshes. In this work, we
extend weight-adjusted DG (WADG) methods to the case of matrix-valued weights,
with the linear elastic wave equation as an application. We present a DG
formulation of the symmetric form of the linear elastic wave equation, with
upwind-like dissipation incorporated through simple penalty fluxes. A
semi-discrete convergence analysis is given, and numerical results confirm the
stability and high order accuracy of WADG for several problems in elastic wave
propagation.
