@Article{IJNAM-16-3,
author = {Wang, Kun and Yau, Wong, Shu and Jizu, Huang},
title = {Analysis of Pollution-Free Approaches for Multi-Dimensional Helmholtz Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {3},
pages = {412--435},
abstract = {<p style="text-align: justify;">Motivated by our recent work about pollution-free difference schemes for solving
Helmholtz equation with high wave numbers, this paper presents an analysis of error estimate for
the numerical solution on the annulus and hollow sphere domains. By applying the weighted-test-function
method and defining two special interpolation operators, we first derive the existence,
uniqueness, stability and the pollution-free error estimate for the one-dimensional problems generated
from a method based on separation of variables. Utilizing the spherical harmonics and
approximations results, we then prove the pollution-free error estimate in $L^2$-norm for multi-dimensional
Helmholtz problems.</p>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-12876},
url = {https://global-sci.com/article/83071/analysis-of-pollution-free-approaches-for-multi-dimensional-helmholtz-equations}
}