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.

引用

页码：2429 / 2445

页数：17

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