We study unique continuation over an interface using a stabilized unfitted finite element method tailored to the conditional stability of the problem. The interface is approximated using an isoparametric transformation of the background mesh and the corresponding geometrical error is included in our error analysis.To counter possible destabilizing effects caused by non-conformity of the discretization and cope with the interface conditions, we introduce adapted regularization terms. This allows to derive error estimates based on conditional stability. Numerical experiments suggest that the presence of an interface seems to be of minor importance for the continuation of the solution beyond the data domain. On the other hand, certain convexity properties of the geometry are crucial as has already been observed for many other problems without interfaces.

翻译：我们研究使用一种针对问题的条件稳定性定制的稳定化非拟合有限元方法在界面上的唯一延拓。界面通过背景网格的等参变换进行近似，相应的几何误差包含在我们的误差分析中。为了应对离散化非协调性可能引起的不稳定效应并处理界面条件，我们引入了自适应正则化项。这使我们能够基于条件稳定性推导误差估计。数值实验表明，界面的存在对解在数据域外的延拓似乎影响较小。另一方面，正如已在许多其他无界面问题中观察到的，几何的某些凸性质至关重要。