A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart-Thomas elements

被引：2
|
作者：
Banz, Lothar [1 ]
Ilyas, Muhammad [2 ]
Lamichhane, Bishnu P. [2 ]
McLean, William [3 ]
Stephan, Ernst P. [4 ]
机构：
[1] Univ Salzburg, Salzburg, Austria
[2] Univ Newcastle, Sch Math & Phys Sci, Callaghan, NSW, Australia
[3] Univ New South Wales, Sch Math & Stat, Sydney, NSW, Australia
[4] Leibniz Univ Hannover, Inst Appl Math, Hannover, Germany
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 37卷 / 03期
关键词：
a priori error estimate; biorthogonal; mixed finite element method; Poisson problem; saddle‐ point problem; APPROXIMATIONS; SPACE;
D O I：
10.1002/num.22722
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We use a three-field mixed formulation of the Poisson equation to develop a mixed finite element method using Raviart-Thomas elements. We use a locally constructed biorthogonal system for Raviart-Thomas finite elements to improve the computational efficiency of the approach. We analyze the existence, uniqueness and stability of the discrete problem and show an a priori error estimate. We also develop an a posteriori error estimate for our formulation. Numerical results are presented to demonstrate the performance of our approach.
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页码：2429 / 2445
页数：17
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