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

A discontinuous least squares finite element method for Helmholtz equations