Weighted overconstrained least-squares mixed finite elements for static and dynamic problems in quasi-incompressible elasticity
Weighted overconstrained least-squares mixed finite elements for static and dynamic problems in quasi-incompressible elasticity
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DOI：
10.1007/s00466-014-1009-1
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发表时间：
2014-04
影响因子：
4.1
通讯作者：
A. Schwarz;K. Steeger;J. Schröder
中科院分区：
文献类型：
--
作者：
A. Schwarz;K. Steeger;J. Schröder
这方面的贡献的主要目标是改进的最小二乘混合有限元的静态和动态问题的准不可压缩弹性的近似质量。与其他变分方法相比，例如Galerkin方法，最小二乘公式的主要缺点是在精度和鲁棒性方面的近似质量不令人满意。在这里，低阶元素尤其受到影响，参见例如[33]。为了避免这些问题，我们引入过约束一阶系统与合适的权重。我们考虑不同的混合最小二乘制剂取决于应力和位移的最大三次多项式插值。对于应力的连续逼近，采用Raviart-Thomas单元，而对于位移，采用标准协调单元。一些数值基准，以验证所提出的配方的性能和效率。
The main goal of this contribution is the improvement of the approximation quality of least-squares mixed finite elements for static and dynamic problems in quasi-incompressible elasticity. Compared with other variational approaches as for example the Galerkin method, the main drawback of least-squares formulations is the unsatisfying approximation quality in terms of accuracy and robustness. Here, lower-order elements are especially affected, see e.g. [33]. In order to circumvent these problems, we introduce overconstrained first-order systems with suited weights. We consider different mixed least-squares formulations depending on stresses and displacements with a maximal cubical polynomial interpolation. For the continuous approximation of the stresses Raviart–Thomas elements are used, while for the displacements standard conforming elements are employed. Some numerical benchmarks are presented in order to validate the performance and efficiency of the proposed formulations.