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Volume 14, Issue 4-5
A Hybridizable Weak Galerkin Method for the Helmholtz Equation with Large Wave Number: $hp$ Analysis

Jiangxing Wang & Zhimin Zhang

Int. J. Numer. Anal. Mod., 14 (2017), pp. 744-761.

Published online: 2017-08

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  • Abstract

In this paper, an $hp$ hybridizable weak Galerkin ($hp$-HWG) method is introduced to solve the Helmholtz equation with large wave number in two and three dimensions. By choosing a specific parameter and using the duality argument, we prove that the proposed method is stable under certain mesh constraint. Error estimate is obtained by using the stability analysis and the duality argument. Several numerical results are provided to confirm our theoretical results.

  • Keywords

Weak Galerkin method, hybridizable method, Helmholtz equation, large wave number, error estimates.

  • AMS Subject Headings

65N15, 65N30, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-744, author = {Jiangxing Wang and Zhimin Zhang}, title = {A Hybridizable Weak Galerkin Method for the Helmholtz Equation with Large Wave Number: $hp$ Analysis}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {4-5}, pages = {744--761}, abstract = {

In this paper, an $hp$ hybridizable weak Galerkin ($hp$-HWG) method is introduced to solve the Helmholtz equation with large wave number in two and three dimensions. By choosing a specific parameter and using the duality argument, we prove that the proposed method is stable under certain mesh constraint. Error estimate is obtained by using the stability analysis and the duality argument. Several numerical results are provided to confirm our theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10059.html} }
TY - JOUR T1 - A Hybridizable Weak Galerkin Method for the Helmholtz Equation with Large Wave Number: $hp$ Analysis AU - Jiangxing Wang & Zhimin Zhang JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 744 EP - 761 PY - 2017 DA - 2017/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10059.html KW - Weak Galerkin method, hybridizable method, Helmholtz equation, large wave number, error estimates. AB -

In this paper, an $hp$ hybridizable weak Galerkin ($hp$-HWG) method is introduced to solve the Helmholtz equation with large wave number in two and three dimensions. By choosing a specific parameter and using the duality argument, we prove that the proposed method is stable under certain mesh constraint. Error estimate is obtained by using the stability analysis and the duality argument. Several numerical results are provided to confirm our theoretical results.

Jiangxing Wang and Zhimin Zhang. (2017). A Hybridizable Weak Galerkin Method for the Helmholtz Equation with Large Wave Number: $hp$ Analysis. International Journal of Numerical Analysis and Modeling. 14 (4-5). 744-761. doi:
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