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A Difference Mixed Finite Element Method for the Three Dimensional Poisson Equation

A Difference Mixed Finite Element Method for the Three Dimensional Poisson Equation

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.

Author Details

Qi Zhang

Pengzhan Huang

Yinnian He