@Article{CiCP-22-133,
author = {Du , Yu and Zhang , Zhimin},
title = {A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number},
journal = {Communications in Computational Physics},
year = {2019},
volume = {22},
number = {1},
pages = {133--156},
abstract = {<p style="text-align: justify;">We study the error analysis of the weak Galerkin finite element method
in [24, 38] (WG-FEM) for the Helmholtz problem with large wave number in two and
three dimensions. Using a modified duality argument proposed by Zhu and Wu, we
obtain the pre-asymptotic error estimates of the WG-FEM. In particular, the error estimates with explicit dependence on the wave number k are derived. This shows that
the pollution error in the broken H<sup>1</sup>-norm is bounded by O(k(kh)<sup>2p</sup>) under mesh condition k<sup>7/2</sup>h<sup>2</sup> ≤C<sub>0</sub> or (kh)<sup>2</sup>+k(kh)<sup>p+1</sup> ≤C<sub>0</sub>, which coincides with the phase error of the
finite element method obtained by existent dispersion analyses. Here h is the mesh
size, p is the order of the approximation space and C<sub>0</sub> is a constant independent of k
and h. Furthermore, numerical tests are provided to verify the theoretical findings and
to illustrate the great capability of the WG-FEM in reducing the pollution effect.</p>},
issn = {1991-7120},
doi = {https://doi.org/ 10.4208/cicp.OA-2016-0121},
url = {http://global-sci.org/intro/article_detail/cicp/13350.html}
}