Analysis of some mixed finite element methods related to reduced integration
Analysis of some mixed finite element methods related to reduced integration
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DOI：
10.1090/s0025-5718-1982-0645657-2
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发表时间：
1982-05
影响因子：
2
通讯作者：
Claes Johnson;J. Pitkäranta
中科院分区：
文献类型：
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作者：
Claes Johnson;J. Pitkäranta
我们证明了以下两个混合有限元方法的误差估计有关减少积分：斯托克斯问题的方法，使用矩形单元的速度和分段常数的压力，和一个方法的板问题，使用双线性近似的横向位移和旋转和分段常数的剪切应力。在Stokes问题的情况下，证明的主要思想是将压力的弱Babuska-Brezzi型稳定性估计与速度的超逼近性质相结合。类似的技术也用于板问题。
We prove error estimates for the following two mixed finite element methods related to reduced integration: A method for Stokes' problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure, and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress. The main idea of the proof in the case of Stokes' problem is to combine a weak Babuska-Brezzi type stability estimate for the pressure with a superapproximability property for the velocities. A similar technique is used in the case of the plate problem.