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Extending the wavenumber-explicit analysis of Chen and Qiu (J Comput Appl Math, 309:145–162, 2017), we analyze the L2-convergence of a least squares method for the Helmholtz equation with wavenumber k. For domains with an analytic boundary, we obtain improved rates in the mesh size h and the polynomial degree p under the scale resolution condition that hk∕p is sufficiently small and \(p/\log k\) is sufficiently large.

Analysis of the hp-Version of a First Order System Least Squares Method for the Helmholtz Equation