Error Estimates for Low-Order Isoparametric Quadrilateral Finite Elements for Plates
Error Estimates for Low-Order Isoparametric Quadrilateral Finite Elements for Plates
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DOI：
10.1137/s0036142902409410
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发表时间：
2003-05
期刊：
影响因子：
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通讯作者：
R. Durán;E. Hernández;L. Hervella-Nieto;E. Liberman;R. Rodríguez
中科院分区：
文献类型：
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作者：
R. Durán;E. Hernández;L. Hervella-Nieto;E. Liberman;R. Rodríguez
本文讨论用Reissner-Mindlin方程模拟板弯曲问题的数值逼近。众所周知，在用有限元法求解这些方程时，为了避免锁定，必须使用某种缩减积分或混合插值。特别是，最广泛使用的程序之一是基于家庭的元素称为MITC（混合插值张量分量）。我们考虑两个最低阶的方法，这个家庭的四边形网格。在温和的假设下，我们得到了这两种方法的最优H1和L2误差估计。这些估计是有效的常数独立的板厚度。我们还获得了板振动问题的近似误差估计。最后，我们报告了一些数值实验，显示了非常好的行为的方法，即使在某些情况下，我们的理论不包括。
This paper deals with the numerical approximation of the bending of a plate modeled by Reissner--Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is based on the family of elements called MITC (mixed interpolation of tensorial components). We consider two lowest-order methods of this family on quadrilateral meshes. Under mild assumptions we obtain optimal H1 and L2 error estimates for both methods. These estimates are valid with constants independent of the plate thickness. We also obtain error estimates for the approximation of the plate vibration problem. Finally, we report some numerical experiments showing the very good behavior of the methods, even in some cases not covered by our theory.