We propose an inverse scheme for acoustic source localization based on solving the corresponding partial differential equation in the frequency domain (Helmholtz equation) by applying the Finite Element (FE) method. This allows us to fully take into account the actual boundary conditions as given in the measurement setup. To recover the source locations, an inverse scheme based on a sparsity promoting Tikhonov functional to match measured (microphone signals) and simulated pressure is proposed. The properties of this inverse scheme and its applicability to source localization in the low frequency range will be demonstrated. © 2018 The Author(s). Published by S. Hirzel Verlag · EAA. This is an open access article under the terms of the Creative Commons Attribution (CC BY 4.0) license (https://creativecommons.org/licenses/by/4.0/).