Coupling of virtual element and boundary element methods for the solution of acoustic scattering problems-Reference-Cited by-同舟云学术

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

Published:2020-12-01 Issue:4 Volume:28 Page:223-245
ISSN:1569-3953
Container-title:Journal of Numerical Mathematics
language:en
Short-container-title:

Author:

Gatica Gabriel N.¹,Meddahi Salim²

Affiliation:

1. CI MA and Departamento de Ingeniería Matemática, Universidad de Concepción , Casilla 160-C , Concepción , Chile

2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo , Calvo Sotelo s/n , Oviedo , España

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Computational Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jnma-2019-0068/pdf

Reference15 articles.

1. B. Ahmad, A. Alsaedi, F. Brezzi, L. D. Marini, and A. Russo, Equivalent projectors for virtual element methods. Comput. Math. Appl. 66 (2013), No. 3, 376–391.

2. L. Beirão da Veiga, F. Brezzi, L. D. Marini, and A. Russo, Virtual element method for general second-order elliptic problems on polygonal meshes. Math. Models Methods Appl. Sci. 26 (2016), No. 4, 729–750.

3. S. C. Brenner, Q. Guan, and L. Y. Sung, Some estimates for virtual element methods. Comput. Methods Appl. Math. 17 (2017), No. 4, 553–574.

4. D. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory Second edition. Applied Mathematical Sciences, Vol. 93. Springer-Verlag, Berlin, 1998.

5. M. Costabel, Symmetric methods for the coupling of finite elements and boundary elements. In: Boundary Elements IX (Eds. C. A. Brebbia, G. Kuhn, and W. L. Wendland), Springer, Berlin, pp. 411–420, (1987).

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