Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates

We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between the exact solutions and truncated expansions at any order.