We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution $u \in H^s$ with $s\in (1,3/2]$. For Nitsche type methods this case requires special handling of the terms involving the normal flux of the exact solution at the the boundary. For Dirichlet boundary conditions the estimates are optimal, whereas in the case of mixed Dirichlet-Neumann boundary conditions they are suboptimal by a logarithmic factor.

中文翻译：

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具有混合边界条件的椭圆问题的 CutFEM 近似的低正则性估计

我们展示了具有混合边界条件的二阶椭圆问题的切割有限元近似的误差估计。误差估计属于低规律类型，我们考虑精确解 $u \in H^s$ 与 $s\in (1,3/2]$ 的情况。对于 Nitsche 类型方法，这种情况需要特殊处理涉及边界处精确解的法向通量的项。对于狄利克雷边界条件，估计是最优的，而在混合狄利克雷-诺依曼边界条件的情况下，它们是对数因子的次优。