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Coupling of virtual element and boundary element methods for the solution of acoustic scattering problems

Gabriel N. Gatica and Salim Meddahi

Abstract

This paper extends the applicability of the combined use of the virtual element method (VEM) and the boundary element method (BEM), recently introduced to solve the coupling of linear elliptic equations in divergence form with the Laplace equation, to the case of acoustic scattering problems in 2D and 3D. The well-posedness of the continuous and discrete formulations are established, and then Cea-type estimates and consequent rates of convergence are derived.

JEL Classification: 65N38; 65N99; 65N12; 65N15

Funding statement: This research was partially supported by ANID-Chile through the project Centro de Modelamiento Matemático (AFB170001) of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal; by Centro de Investigación en Ingeniería Matemática (CI2MA), Universidad de Concepción; and by Spain’s Ministry of Economy Project MTM2017-87162-P.

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Received: 2019-07-12
Revised: 2020-04-18
Accepted: 2020-04-28
Published Online: 2020-12-11
Published in Print: 2020-12-16

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