Year: 2017
Author: Yu Du, Zhimin Zhang
Communications in Computational Physics, Vol. 22 (2017), Iss. 1 : pp. 133–156
Abstract
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 H1-norm is bounded by O(k(kh)2p) under mesh condition k7/2h2 ≤C0 or (kh)2+k(kh)p+1 ≤C0, 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 C0 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/ 10.4208/cicp.OA-2016-0121
Communications in Computational Physics, Vol. 22 (2017), Iss. 1 : pp. 133–156
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Weak Galerkin finite element method Helmholtz equation large wave number stability error estimates.