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A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart–Thomas elements
Numerical Methods for Partial Differential Equations ( IF 2.1 ) Pub Date : 2020-12-21 , DOI: 10.1002/num.22722
Lothar Banz 1 , Muhammad Ilyas 2 , Bishnu P. Lamichhane 2 , William McLean 3 , Ernst P. Stephan 4
Affiliation  

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.

中文翻译:

使用带有Raviart–Thomas元素的双正交系统的Poisson问题的混合有限元方法

我们使用Poisson方程的三场混合公式来开发使用Raviart–Thomas元素的混合有限元方法。我们对Raviart–Thomas有限元使用本地构造的双正交系统,以提高该方法的计算效率。我们分析了离散问题的存在性,唯一性和稳定性,并给出了先验误差估计。我们还为我们的配方开发了后验误差估计。数值结果表明了我们方法的性能。
更新日期:2020-12-21
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