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.

引用

页数：22

共 50 条

[41] Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
Holst, M.
McCammon, J. A.
Yu, Z.
Zhou, Y. C.
Zhu, Y.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2012, 11 (01) : 179 - 214
[42] A Spectral Mortar Element Discretization of the Poisson Equation with Mixed Boundary Conditions
Zakaria Belhachmi
Andreas Karageorghis
Journal of Scientific Computing, 2007, 30 : 275 - 299
[43] A spectral mortar element discretization of the Poisson equation with mixed boundary conditions
Belhachmi, Zakaria
Karageorghis, Andreas
JOURNAL OF SCIENTIFIC COMPUTING, 2007, 30 (02) : 275 - 299
[44] On a finite element method for three-dimensional unsteady compressible viscous flows
Liu, BY
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2004, 20 (03) : 432 - 449
[45] A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation
Zhang, Yaping
Cao, Jiliang
Bu, Weiping
Xiao, Aiguo
INTERNATIONAL JOURNAL OF MODELING SIMULATION AND SCIENTIFIC COMPUTING, 2020, 11 (02)
[46] Higher order difference numerical analyses of a 2D Poisson equation by the interpolation finite difference method and calculation error evaluation
Fukuchi, Tsugio
AIP ADVANCES, 2020, 10 (12)
[47] Compact finite difference schemes of arbitrary order for the Poisson equation in arbitrary dimensions
Erwan Deriaz
BIT Numerical Mathematics, 2020, 60 : 199 - 233
[48] Local boundary element based a new finite difference representation for Poisson equations
Kim, Sangdong
Ahn, Soyoung
Kim, Philsu
APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (12) : 5186 - 5198
[49] Compact finite difference schemes of arbitrary order for the Poisson equation in arbitrary dimensions
Deriaz, Erwan
BIT NUMERICAL MATHEMATICS, 2020, 60 (01) : 199 - 233
[50] Error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems
Hou, Tianliang
Liu, Chunmei
Yang, Yin
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (04) : 714 - 726

← 1 2 3 4 5 →