full
search.png

Search

close.png

Cancel

arrow
Volume 22, Issue 1
A Difference Virtual Element Method for the 3D Elliptic Equation with the Variable Coefficient on General Cylindrical Domains

Lulu Li, Yinnian He & Xinlong Feng

DOI: 10.4208/ijnam2025-1005

Int. J. Numer. Anal. Mod., 22 (2025), pp. 96-112.

Published online: 2024-11

Preview Full PDF 26 212

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In this paper, we present and analysis a difference virtual element method (DVEM) for the three dimensional (3D) elliptic equation on general cylindrical domains. This method combines the dimension splitting method and operator splitting technique to transform the virtual element solution of 3D elliptic equation into a series of virtual element solution of 2D elliptic equation based on $(x, y)$ plane, where the central difference discretization is adopted in the $z$-direction. This allows us to solve partial differential equations on cylindrical domains at the low cost in mesh generation compared with 3D virtual element method. The $H^1$-norm error estimation of the DVEM is analysed in this paper. Finally, some numerical examples are performed to verify the theoretical predictions and showcase the efficiency of the proposed method.

  • Keywords

3D elliptic equation, difference virtual element, virtual element, cylindrical domain, error analysis.

  • AMS Subject Headings

65N06, 65N15, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{IJNAM-22-96, author = {Li , LuluHe , Yinnian and Feng , Xinlong}, title = {A Difference Virtual Element Method for the 3D Elliptic Equation with the Variable Coefficient on General Cylindrical Domains}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {22}, number = {1}, pages = {96--112}, abstract = {

In this paper, we present and analysis a difference virtual element method (DVEM) for the three dimensional (3D) elliptic equation on general cylindrical domains. This method combines the dimension splitting method and operator splitting technique to transform the virtual element solution of 3D elliptic equation into a series of virtual element solution of 2D elliptic equation based on $(x, y)$ plane, where the central difference discretization is adopted in the $z$-direction. This allows us to solve partial differential equations on cylindrical domains at the low cost in mesh generation compared with 3D virtual element method. The $H^1$-norm error estimation of the DVEM is analysed in this paper. Finally, some numerical examples are performed to verify the theoretical predictions and showcase the efficiency of the proposed method.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1005}, url = {http://global-sci.org/intro/article_detail/ijnam/23568.html} }
TY - JOUR T1 - A Difference Virtual Element Method for the 3D Elliptic Equation with the Variable Coefficient on General Cylindrical Domains AU - Li , Lulu AU - He , Yinnian AU - Feng , Xinlong JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 96 EP - 112 PY - 2024 DA - 2024/11 SN - 22 DO - http://doi.org/10.4208/ijnam2025-1005 UR - https://global-sci.org/intro/article_detail/ijnam/23568.html KW - 3D elliptic equation, difference virtual element, virtual element, cylindrical domain, error analysis. AB -

In this paper, we present and analysis a difference virtual element method (DVEM) for the three dimensional (3D) elliptic equation on general cylindrical domains. This method combines the dimension splitting method and operator splitting technique to transform the virtual element solution of 3D elliptic equation into a series of virtual element solution of 2D elliptic equation based on $(x, y)$ plane, where the central difference discretization is adopted in the $z$-direction. This allows us to solve partial differential equations on cylindrical domains at the low cost in mesh generation compared with 3D virtual element method. The $H^1$-norm error estimation of the DVEM is analysed in this paper. Finally, some numerical examples are performed to verify the theoretical predictions and showcase the efficiency of the proposed method.

Li , LuluHe , Yinnian and Feng , Xinlong. (2024). A Difference Virtual Element Method for the 3D Elliptic Equation with the Variable Coefficient on General Cylindrical Domains. International Journal of Numerical Analysis and Modeling. 22 (1). 96-112. doi:10.4208/ijnam2025-1005
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard