TY - JOUR
T1 - Difference Finite Element Methods Based on Different Discretization Elements for the Four-Dimensional Poisson Equation
AU - Liu , Yaru
AU - Feng , Xinlong
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 415
EP - 438
PY - 2025
DA - 2025/01
SN - 15
DO - http://doi.org/10.4208/eajam.2023-233.200224
UR - https://global-sci.org/intro/article_detail/eajam/23756.html
KW - 4D Poisson equation, difference finite element method, hexahedral element, pentahedral element, tetrahedral element.
AB - <p style="text-align: justify;">This paper proposes difference finite element (DFE) methods for the Poisson
equation in a four-dimensional (4D) region $ω × (0, L_4
).$ The method converts the Poisson equation in a 4D region into a series of three-dimensional (3D) subproblems by the
finite difference discretization in $(0, L_4)$ and deals with the 3D subproblems by the finite
element discretization in $ω.$ In performing the finite element discretization, we select
different discretization elements in the region $ω:$ hexahedral, pentahedral, and tetrahedral elements. Moreover, we prove the stability of the DFE solution $u_h$ and deduce the
first-order convergence of $u_h$ with respect to the exact solution $u$ under $H^1$-error. Finally,
three numerical examples are given to verify the accuracy and effectiveness of the DFE
method.</p>