In this paper, some partial penalized immersed finite element methods (PPIFEMs) are proposed and analyzed for solving elasticity interface problems. Through verifying the inverse trace inequality on the interface edges, the optimal convergence in the energy norm is derived. A new test function is constructed to obtain the discrete inf–sup condition of the penalty-free nonsymmetric PPIFEM and is utilized in the proof of the optimal convergence. Furthermore, the effect of the Lamé parameters on convergence is also studied. Various numerical examples and comparisons are provided to confirm the theoretical results.

中文翻译：

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弹性界面问题的部分惩罚式IFE方法和收敛性分析

针对弹性界面问题，本文提出并分析了部分惩罚沉浸式有限元方法（PPIFEMs）。通过验证界面边缘的逆轨迹不等式，得出能量范数的最佳收敛。构造了一个新的测试函数来获得无罚非对称PPIFEM的离散inf-sup条件，并用于证明最佳收敛。此外，还研究了Lamé参数对收敛的影响。提供各种数值示例和比较以证实理论结果。