TY - JOUR
T1 - Weak Galerkin Method for the Helmholtz Equation with DtN Boundary Condition
AU - Hu , Qingjie
AU - He , Yinnian
AU - Wang , Kun
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 643
EP - 661
PY - 2020
DA - 2020/08
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/17873.html
KW - Helmholtz equation, weak Galerkin method, Dirichlet to Neumann operator, error
estimates.
AB - <p style="text-align: justify;">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.</p>