Zhizhuo Zhang , Mikaël Barboteu , Xiaobing Nie , Serge Dumont , Mahmoud Abdel-Aty , Jinde Cao
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引用次数: 0
Abstract
With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent saddle point problems with interlayer Tresca friction conditions and the mixed finite element method are proposed and analyzed. Then, the convergence of the numerical solution of the mixed finite element method is theoretically proven, and the corresponding algebraic dual algorithm is provided. Finally, through numerical experiments, the mixed finite element method is not only compared with the layer decomposition method, but also its convergence relationship with respect to the spatial discretization parameter is verified.
随着多层弹性系统在工程力学领域的发展，相应的变分不等式理论和算法设计得到了更多的关注和研究。本研究提出并分析了一类具有层间 Tresca 摩擦条件的等效鞍点问题和混合有限元法。然后，从理论上证明了混合有限元法数值解的收敛性，并提供了相应的代数对偶算法。最后，通过数值实验，不仅比较了混合有限元法与层分解法，还验证了其与空间离散参数 H 的收敛关系。
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