A priori error estimates of the DtN-FEM for the transmission problem in acoustics

详细信息    查看全文

• 作者：Hongrui Geng^a ; ^{ghr0313@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; Tao Yin^a ; ^{taoyin_cqu@163.com" class="auth_mail" title="E-mail the corresponding author} ; Liwei Xu^a ; ^b ; ^{xul@cqu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Dirichlet-to-Neumann mapping ; Finite element methods ; Acoustic transmission problems ; Fourier series
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：1-17
• 全文大小：1130 K

文摘

This paper is concerned with a variational approach solving the two-dimensional acoustic transmission problems. The original problem is reduced to an equivalent nonlocal boundary value problem by introducing an exact Dirichlet-to-Neumann (DtN) mapping in terms of Fourier expansion series on an artificial boundary. Uniqueness and existence of solutions in appropriate Sobolev spaces are established for the corresponding variational problem and its modification due to the truncation of DtN mapping. A priori error estimates containing the effects of both element meshsize and truncation order of series for the finite element approximation are derived. Numerical experiments are also presented to illustrate the efficiency and accuracy of the numerical scheme.