Abstract

In two dimensions, we propose and analyze an a posteriori error estimator for the acoustic spectral problem based on the virtual element method in H(div;?). 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 Lsp2-norm. We provide numerical results to assess the performance of the proposed error estimator. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.