The Enriched Crouzeix–Raviart Elements are Equivalent to the Raviart–Thomas Elements
The Enriched Crouzeix–Raviart Elements are Equivalent to the Raviart–Thomas Elements
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DOI：
10.1007/s10915-014-9899-9
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发表时间：
2014-01
影响因子：
2.5
通讯作者：
Jun-Jue Hu;R. Ma
中科院分区：
文献类型：
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作者：
Jun-Jue Hu;R. Ma
对于泊松模型问题和任意维的Stokes问题，本文证明了富Crouzeix-Raviart单元实际上与一阶Raviart-Thomas单元相同，即它们产生相同的离散应力。这一结果改进了先前文献的结果，即在二维情况下，一阶Raviart-Thomas单元的应力分段常数投影等于Crouzeix-Raviart单元的应力分段常数投影。对于拉普拉斯算子的特征值问题，证明了富Crouzeix-Raviart元在高阶项上的误差与一阶Raviart-Thomas元的误差相等。
For both the Poisson model problem and the Stokes problem in any dimension, this paper proves that the enriched Crouzeix–Raviart elements are actually identical to the first order Raviart–Thomas elements in the sense that they produce the same discrete stresses. This result improves the previous result in literature which, for two dimensions, states that the piecewise constant projection of the stress by the first order Raviart–Thomas element is equal to that by the Crouzeix–Raviart element. For the eigenvalue problem of the Laplace operator, this paper proves that the error of the enriched Crouzeix–Raviart element is equivalent to that of the first order Raviart–Thomas element up to higher order terms.