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To solve wave propagation problems involving change of medium, many authors employ the generalized finite element method with plane wave enrichment and Lagrange multipliers to ensure interface constraints. However this approach produces ill conditioned and nonpositive definite systems, making it hard to solve. This paper presents an approach based on the mortar element method that substitutes the Lagrange multipliers with the advantage of generating sparse and positive definite systems. Various numerical aspects affecting the generalized finite element method efficiency are analyzed by solving a 2-D scattering problem.