THE NONCONFORMING VIRTUAL ELEMENT METHOD
THE NONCONFORMING VIRTUAL ELEMENT METHOD
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DOI：
10.1051/m2an/2015090
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发表时间：
2016-05-01
影响因子：
1.9
通讯作者：
Manzini, Gianmarco
中科院分区：
文献类型：
--
作者：
de Dios, Blanca Ayuso;Lipnikov, Konstantin;Manzini, Gianmarco
介绍了求解二阶椭圆问题的一种新的近似方法--虚元法。我们提出了新的元素在二维和三维的建设，突出的主要区别与符合VEM和经典的非线性有限元方法。我们提供了误差分析，并建立了一个家庭的拟有限差分方法的等价性。数值实验验证了理论的正确性，验证了所提方法的有效性.
We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods. Numerical experiments verify the theory and validate the performance of the proposed method.