In this paper, we introduce an abstract setting for the convergence analysis of the virtual element approximation of an acoustic vibration problem. We discuss the effect of the stabilization parameters and remark that in some cases it is possible to achieve optimal convergence without the need of any stabilization. This statement is rigorously proved for the lowest order triangular element and supported by several numerical experiments.
On the stabilization of a virtual element method for an acoustic vibration problem
Boffi, Daniele;Gastaldi, Lucia
2025-01-01
Abstract
In this paper, we introduce an abstract setting for the convergence analysis of the virtual element approximation of an acoustic vibration problem. We discuss the effect of the stabilization parameters and remark that in some cases it is possible to achieve optimal convergence without the need of any stabilization. This statement is rigorously proved for the lowest order triangular element and supported by several numerical experiments.File in questo prodotto:
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