期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 276, 期 -, 页码 122-148出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2014.03.015
关键词
Non-reflecting boundary condition; Open boundary condition; Artificial boundary condition; Wave equation; Stabilized finite element methods; Variational multi-scale method
资金
- Ministerio de Educacion, Cultura y Deporte, Programa de Formacion del Profesorado Universitario (FPU), in Spain [AP2010-0563]
- FP7 (project Eunison) [308874]
- ICREA Academia Program from the Catalan Government
- European Research Council [258443]
- European Research Council (ERC) [258443] Funding Source: European Research Council (ERC)
In this paper we develop numerical approximations of the wave equation in mixed form supplemented with non-reflecting boundary conditions (NRBCs) of Sommerfeld-type on artificial boundaries for truncated domains. We consider three different variational forms for this problem, depending on the functional space for the solution, in particular, in what refers to the regularity required on artificial boundaries. Then, stabilized finite element methods that can mimic these three functional settings are described. Stability and convergence analyses of these stabilized formulations including the NRBC are presented. Additionally, numerical convergence test are evaluated for various polynomial interpolations, stabilization methods and variational forms. Finally, several benchmark problems are solved to determine the accuracy of these methods in 2D and 3D. (C) 2014 Elsevier B.V. All rights reserved.
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