Year: 2019
Author: Kun Wang, Yau Shu Wong, Jizu Huang
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 3 : pp. 412–435
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-12876
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 3 : pp. 412–435
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Helmholtz equation error estimate finite difference method polar and spherical coordinates pollution-free scheme.