@Article{CiCP-23-3,
author = {},
title = {Dispersion Error Analysis of Stable Node-Based Finite Element Method for the Helmholtz Equation},
journal = {Communications in Computational Physics},
year = {2018},
volume = {23},
number = {3},
pages = {795--821},
abstract = {<p style="text-align: justify;">Numerical dispersion error is inevitable when the finite element method is
employed to simulate acoustic problems. Studies have shown that the dispersion error
is essentially rooted at the &quot;overly-stiff&quot; property of the standard FEM model. To
reduce the dispersion error effectively, a discrete model that provides a proper softening
effects is needed. Thus, the stable node-based smoothed finite element method
(SNS-FEM) which contains a stable item is presented. In this paper, the SNS-FEM is
investigated in details with respect to the pollution effect. Different kinds of meshes
are employed to analyze the relationship between the dispersion error and the parameter
involved in the stable item. To ensure the SNS-FEM can be applied to the practical
engineering problems effectively, the relationship is finally constructed based on the
hexagonal patch for the commonly used unstructured mesh is very similar to it. By
minimizing the discretization error, an optimal parameter equipped in this novel SNSFEM
is formulated. Both theoretical analysis and numerical examples demonstrate
that the SNS-FEM with the optimal parameter reduces the dispersion error significantly compared with the FEM and the well performed GLS, especially for mid- and
high-wave number problems.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0191},
url = {https://global-sci.com/article/80031/dispersion-error-analysis-of-stable-node-based-finite-element-method-for-the-helmholtz-equation}
}