Year: 2020
Author: Qingjie Hu, Yinnian He, Kun Wang
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 5 : pp. 643–661
Abstract
In this article, we consider a weak Galerkin finite element method for the two dimensional exterior Helmholtz problem. After introducing a nonlocal boundary condition by means of the exact Dirichlet to Neumann (DtN) operator for the exterior problem, we prove that the existence and uniqueness of the weak Galerkin finite element solution for this problem. Then, applying some projection techniques, we establish a priori error estimate, which include the effect of truncation of the DtN boundary condition as well as the spatial discretization. Finally, some numerical examples are presented to confirm the theoretical predictions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-17873
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 5 : pp. 643–661
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Helmholtz equation weak Galerkin method Dirichlet to Neumann operator error estimates.