@Article{EAJAM-15-415,
author = {Liu , Yaru and Feng , Xinlong},
title = {Difference Finite Element Methods Based on Different Discretization Elements for the Four-Dimensional Poisson Equation},
journal = {East Asian Journal on Applied Mathematics},
year = {2025},
volume = {15},
number = {2},
pages = {415--438},
abstract = {<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>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2023-233.200224},
url = {http://global-sci.org/intro/article_detail/eajam/23756.html}
}