1 results
A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number
- Part of
-
- Journal:
- Communications in Computational Physics / Volume 22 / Issue 1 / July 2017
- Published online by Cambridge University Press:
- 03 May 2017, pp. 133-156
- Print publication:
- July 2017
-
- Article
- Export citation
-
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
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.
under mesh condition 