Mathematical Models and Methods in Applied Sciences ( IF 3.6 ) Pub Date : 2021-12-20 Franco Dassi, Carlo Lovadina, Michele Visinoni
In this paper, we extend the hybridization procedure proposed in [D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates, ESAIM Math. Model. Numer. Anal.19 (1985) 7–32] to the Virtual Element Method for linear elasticity problems based on the Hellinger–Reissner principle. To illustrate such a technique, we focus on a specific 2D scheme, but other methods and 3D problems can be considered as well. We also show how to design a better approximation of the displacement field using a straightforward post-processing procedure. The numerical experiments confirm the theory for both two and three-dimensional problems.
中文翻译:
用于线性弹性问题的虚拟元方法的混合
在本文中,我们扩展了 [D. N. Arnold 和 F. Brezzi,混合和非一致性有限元方法:实施、后处理和误差估计,ESAIM 数学。模型。数字。肛门。19 (1985) 7-32] 到基于 Hellinger-Reissner 原理的线性弹性问题的虚拟元素方法。为了说明这种技术,我们专注于特定的 2D 方案,但也可以考虑其他方法和 3D 问题。我们还展示了如何使用简单的后处理程序设计更好的位移场近似值。数值实验证实了二维和三维问题的理论。