We investigate the piecewise linear nonconforming Crouzeix–Raviart and the lowest order Raviart–Thomas finite-element methods for the Poisson problem on three-dimensional anisotropic meshes. We first give error estimates of the Crouzeix–Raviart and the Raviart–Thomas finite-element approximate problems. We next present the equivalence between the Raviart–Thomas finite-element method and the enriched Crouzeix–Raviart finite-element method. We emphasize that we do not impose either shape-regular or maximum-angle condition during mesh partitioning. Numerical results confirm the results that we obtained.

中文翻译：

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违反最大角度条件的各向异性网格上的Crouzeix–Raviart和Raviart–Thomas有限元误差分析

我们研究了三维各向异性网格上泊松问题的分段线性不合格Crouzeix-Raviart和最低阶Raviart-Thomas有限元方法。我们首先给出Crouzeix–Raviart和Raviart–Thomas有限元近似问题的误差估计。接下来，我们介绍Raviart–Thomas有限元方法与丰富的Crouzeix–Raviart有限元方法之间的等价关系。我们强调，在网格划分期间，我们不施加形状规则或最大角度条件。数值结果证实了我们获得的结果。