Weak Galerkin Method for the Helmholtz Equation with DtN Boundary Condition

Weak Galerkin Method for the Helmholtz Equation with DtN Boundary Condition

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.

Author Details

Qingjie Hu

Yinnian He

Kun Wang