Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition
Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition
复制标题
违反最大角度条件的各向异性网格的 Crouzeix-Raviart 和 Raviart-Thomas 有限元误差分析
DOI：
10.1007/s13160-020-00455-7
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发表时间：
2021
影响因子：
0.9
通讯作者：
Tsuchiya Takuya
中科院分区：
文献类型：
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作者：
Ishizaka Hiroki;Kobayashi Kenta;Tsuchiya Takuya
我们研究了三维各向异性网格上泊松问题的分段线性非一致性 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 有限元方法和丰富的 Crouzeix-Raviart 有限元方法之间的等价性。我们强调，在网格划分过程中，我们不会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。
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.