TY - JOUR
T1 - A Difference Finite Element Method for Convection-Diffusion Equations in Cylindrical Domains
AU - Shi , Chenhong
AU - He , Yinnian
AU - Sheen , Dongwoo
AU - Feng , Xinlong
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 407
EP - 430
PY - 2024
DA - 2024/05
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1016
UR - https://global-sci.org/intro/article_detail/ijnam/23129.html
KW - Convection-diffusion equation, difference finite element method, cylindrical domain, error estimates.
AB - <p style="text-align: justify;">In this paper, we consider 3D steady convection-diffusion equations in cylindrical
domains. Instead of applying the finite difference methods (FDM) or the finite element methods
(FEM), we propose a difference finite element method (DFEM) that can maximize good applicability and efficiency of both FDM and FEM. The essence of this method lies in employing the
centered difference discretization in the $z$-direction and the finite element discretization based on
the $P_1$ conforming elements in the $(x, y)$ plane. This allows us to solve partial differential equations on complex cylindrical domains at lower computational costs compared to applying the 3D
finite element method. We derive stability estimates for the difference finite element solution and
establish the explicit dependence of $H_1$ error bounds on the diffusivity, convection field modulus,
and mesh size. Finally, we provide numerical examples to verify the theoretical predictions and
showcase the accuracy of the considered method.</p>