A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number

作者：Du Yu; Zhang Zhimin^*

来源：Communications in Computational Physics, 2017, 22(1): 133-156.

DOI：10.4208/cicp.OA-2016-0121

• Weak Galerkin finite element method
• Helmholtz equation
• large wave number
• stability
• error estimates

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-1-norm is bounded by O(k(kh)(2p)) under mesh condition k(7/2)h(2) <= C-0 or (kh)(2) + k(kh) (p+ 1) <= C-0, 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-0 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.

• 出版日期2017-7
• 单位北京计算科学研究中心