  This paper analyzes a space-time finite element method for fractional wave
problems. The method uses a Petrov-Galerkin type time-stepping scheme to
discretize the time fractional derivative of order $ \gamma $ ($1<\gamma<2$).
We establish the stability of this method, and derive the optimal convergence
in the $ H^1(0,T;L^2(\Omega)) $-norm and suboptimal convergence in the discrete
$ L^\infty(0,T;H_0^1(\Omega)) $-norm. Furthermore, we discuss the performance
of this method in the case that the solution has singularity at $ t= 0 $, and
show that optimal convergence rate with respect to the $ H^1(0,T;L^2(\Omega))
$-norm can still be achieved by using graded grids in the time discretization.
Finally, numerical experiments are performed to verify the theoretical results.
