This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated weak form for the interface problem. This article further establishes a critical trace inequality for the Frenet IFE functions. These features enable us to prove that the Frenet IFE method converges optimally under mesh refinement in both $L^2$ and energy norms.

翻译：本文对最近提出的Frenet浸入有限元（IFE）方法进行了误差分析。该方法采用的Frenet IFE空间被构造为在局部上符合界面问题对应弱形式函数空间的要求。本文进一步建立了Frenet IFE函数的关键迹不等式。这些特性使我们能够证明，在网格细化过程中，Frenet IFE方法在$L^2$范数和能量范数下均能达到最优收敛阶。