A posteriori virtual element method for the acoustic vibration problem

07/26/2022

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by   Felipe Lepe, et al.

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In two dimensions, we propose and analyze an a posteriori error estimator for the acoustic spectral problem based on the virtual element method in (̋÷;Ω). Introducing an auxiliary unknown, we use the fact that the primal formulation of the acoustic problem is equivalent to a mixed formulation, in order to prove a superconvergence result, necessary to despise high order terms. Under the virtual element approach, we prove that our local indicator is reliable and globally efficient in the Ł^2-norm. We provide numerical results to assess the performance of the proposed error estimator.