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

被引：0
|
作者：
Zhang, Qi [1 ]
Huang, Pengzhan [1 ]
He, Yinnian [1 ]
机构：
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
来源：
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2024年
关键词：
Poisson equation; difference mixed finite element; error estimate; inf-sup condition; finite element pair; CRANK-NICOLSON SCHEME; PRIMITIVE EQUATIONS; ELLIPTIC-EQUATIONS; SUPERCONVERGENCE;
D O I：
10.4208/eajam.2023-247.050224
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A difference mixed finite element method based on the finite element pair (( P 0 x P 1 ), ( P 0 x P 1 ), ( P 1 x P 0 ))x( P 1 x 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 )x P 1- element in ( x , y )-plane and a finite difference discretization based on ( P 1 , P 1 , P 0 ) x 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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页数：22
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