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.

翻译：我们建议了一种不连续最小平方块的限定元素方法,用于解决Helmholtz方程式。该方法基于L2规范最低方块,在内部面以及边界条件的连续性不强的情况下,以L2规范最低方块为基础。我们尽量缩小不连续的多元空间的功能,以寻求数字解决方案。确定了我们方法的波数明确误差估计值。实现了固定波数能源标准的最佳趋同率。最小方块功能自然可以作为h-适应程序中的后方测量器。由于使用了不连续元素,因此实施代码是方便的。提出了两个和三个层面的数值结果,以核实错误估计值。