一类虚非协调有限元及其在泊松方程中的应用

Int. J. Math. Model. Numer. Optimisation Pub Date : 2022-01-01 DOI:10.1504/ijmmno.2022.10045640

H. El-Otmany

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引用次数: 0

摘要

本文从二维和三维的经典Crouzeix-Raviart单元出发，发展并分析了非协调有限元的虚拟类。我们着重讨论泊松方程的理论和数值结果。我们证明了离散问题是稳定的，并且先验误差估计是最优的。给出了两个数值试验来验证理论结果。

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A virtual class of non-conforming finite elements and its applications to Poisson's equation

In this paper, we develop and analyze the virtual class of nonconforming Finite Element inspired from the classical Crouzeix-Raviart element in two and three-dimensions. We focus on Poisson’s equation for theoretical and numerical results. We show that the discrete problem is stable and the a priori error estimates are optimal. Two numerical tests are presented to demonstrate the theoretical results.

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Int. J. Math. Model. Numer. Optimisation

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