We describe a strategy for implicit a posteriori error estimation in cut finite elements. Our approach is based on the definition of local residual-driven corrector problems that use a local order elevation of the finite element space to construct a correction of the current approximation. The recovered higher-order accurate approximation is then used to construct error estimation in energy norm. We discuss implications of this scheme in the presence of cut elements, for instance regarding the construction of local corrector regions or the imposition of local boundary conditions. Combining the estimator with the finite cell method and a mesh refinement scheme, we numerically demonstrate its effectivity in terms of predicting the true error and its suitability to steer mesh adaptivity. Our results confirm that the estimation achieves the same effectivity in cut meshes as in standard boundary-fitted meshes, irrespective of the polynomial degree.

中文翻译：

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在切割有限元中隐含后验误差估计

我们描述了一种在切割有限元中隐式后验误差估计的策略。我们的方法基于局部残差驱动校正器问题的定义，该问题使用有限元空间的局部阶次高程来构建当前近似值的校正。然后使用恢复的高阶精确近似来构建能量范数中的误差估计。我们讨论了在存在切割元素的情况下该方案的含义，例如关于局部校正器区域的构建或局部边界条件的施加。将估计器与有限单元法和网格细化方案相结合，我们从数值上证明了它在预测真实误差方面的有效性及其对引导网格自适应性的适用性。