  We propose a discontinuous least squares finite element method for solving
the Helmholtz equation. The method is based on the L2 norm least squares
functional with the weak imposition of the continuity across the interior faces
as well as the boundary conditions. We minimize the functional over the
discontinuous polynomial spaces to seek numerical solutions. The wavenumber
explicit error estimates to our method are established. The optimal convergence
rate in the energy norm with respect to a fixed wavenumber is attained. The
least squares functional can naturally serve as a posteriori estimator in the
h-adaptive procedure. It is convenient to implement the code due to the usage
of discontinuous elements. Numerical results in two and three dimensions are
presented to verify the error estimates.
