A Difference Virtual Element Method for the 3D Elliptic Equation with the Variable Coefficient on General Cylindrical Domains
Year: 2025
Author: Lulu Li, Yinnian He, Xinlong Feng
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 1 : pp. 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 H1-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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1005
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 1 : pp. 96–112
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: 3D elliptic equation difference virtual element virtual element cylindrical domain error analysis.
Author Details
Lulu Li Email
Yinnian He Email
Xinlong Feng Email