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 - <p style="text-align: justify;">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.</p>