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We present an a posteriori error estimator for the approximations of the acoustic vibration modes obtained by a finite element method which does not present spurious or circulation modes for non zero frequencies. We prove that the proposed estimator is equivalent to the error in the approximation of the eigenvectors up to higher order terms with constants independent of the eigenvalues. Numerical results for some test examples are presented which show the good behavior of the estimator when it is used as local error indicator for adaptive refinement.

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