Year: 2025
Author: Qi Zhang, Pengzhan Huang, Yinnian He
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 268–289
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-247.050224
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 268–289
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Poisson equation difference mixed finite element error estimate inf-sup condition finite element pair.