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 given. 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 $H$ is verified.

翻译：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与算法设计受到越来越多的关注与研究。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及其混合有限元方法。随后，从理论上证明了混合有限元方法数值解的收敛性，并给出了相应的代数对偶算法。最后通过数值实验，不仅将混合有限元方法与层分解法进行了对比，还验证了其关于空间离散参数$H$的收敛关系。