TY - JOUR
T1 - A Difference Mixed Finite Element Method for the Three Dimensional Poisson Equation
AU - Zhang , Qi
AU - Huang , Pengzhan
AU - He , Yinnian
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 268
EP - 289
PY - 2025
DA - 2025/01
SN - 15
DO - http://doi.org/10.4208/eajam.2023-247.050224
UR - https://global-sci.org/intro/article_detail/eajam/23750.html
KW - Poisson equation, difference mixed finite element, error estimate, inf-sup condition, finite element pair.
AB - <p style="text-align: justify;">A difference mixed finite element method based on the finite element pair $((P_0×P_1),$$(P_0×P_1),$$(P_1×P_0))×(P_1×P_1)$ for the three dimensional Poisson equation is studied. The method combines a mixed finite element discretization based on $(P_0
, P_0
, P_1
)×P_1$-element in $(x,y)$-plane and a finite difference discretization based on $(P_1,P_1,P_0)×P_1$-element in $z$-direction. This allows to transmit the finite element solution of the three
dimensional Poisson equation in the direction $(x, y, z)$ into a series of finite element solution of the two dimensional Poisson equation in the direction $(x, y).$ Moreover, error
estimates for the discrete approximation are derived. Numerical tests show the accuracy
and efficiency for the method proposed.</p>