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We propose a new finite element method for Helmholtz equation in thesituation where an acoustically permeable interface is embedded in thecomputational domain. A variant of Nitsche's method, different from thestandard one, weakly enforces the impedance conditions for transmission throughthe interface. As opposed to a standard finite-element discretization of theproblem, our method seamlessly handles a complex-valued impedance function $Z$that is allowed to vanish. In the case of a vanishing impedance, the proposedmethod reduces to the classic Nitsche method to weakly enforce continuity overthe interface. We show stability of the method, in terms of a discreteG{\aa}rding inequality, for a quite general class of surface impedancefunctions, provided that possible surface waves are sufficiently resolved bythe mesh. Moreover, we prove an a priori error estimate under the assumptionthat the absolute value of the impedance is bounded away from zero almosteverywhere. Numerical experiments illustrate the performance of the method fora number of test cases in 2D and 3D with different interface conditions.

A Nitsche-type Method for Helmholtz Equation with an Embedded Acoustically Permeable Interface