  A high order cut finite element method is formulated for solving the elastic
wave equation. Both a single domain problem and an interface problem are
treated. The boundary or interface are allowed to cut through the background
mesh. To avoid problems with small cuts, stabilizing terms are added to the
bilinear forms corresponding to the mass and stiffness matrix. The stabilizing
terms penalize jumps in normal derivatives over the faces of the elements cut
by the boundary/interface. This ensures a stable discretization independently
of how the boundary/interface cuts the mesh. Nitsche's method is used to
enforce boundary and interface conditions, resulting in symmetric bilinear
forms. As a result of the symmetry, an energy estimate can be made and optimal
order a priori error estimates are derived for the single domain problem.
Finally, numerical experiments in two dimensions are presented that verify the
order of accuracy and stability with respect to small cuts.
