Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error in the solution of a differential problem in which it is defined. In this work, we extend the results from [1] by studying the case of domains containing an arbitrary number of distinct Neumann features, and by performing an analysis on Poisson's, linear elasticity, and Stokes' equations. We introduce a simple, computationally cheap, reliable, and efficient a posteriori estimator of the geometrical defeaturing error. Moreover, we also introduce a geometric refinement strategy that accounts for the defeaturing error: Starting from a fully defeatured geometry, the algorithm determines at each iteration step which features need to be added to the geometrical model to reduce the defeaturing error. These important features are then added to the (partially) defeatured geometrical model at the next iteration, until the solution attains a prescribed accuracy. A wide range of two- and three-dimensional numerical experiments are finally reported to illustrate this work.

翻译：针对计算域进行局部修改通常是为了简化网格生成过程并降低计算成本和内存需求。然而，移除几何特征往往会在其所定义的微分问题求解中引入不可忽略的误差。本研究在文献[1]基础上进行拓展，研究了包含任意数量不同Neumann特征的计算域情形，并针对泊松方程、线弹性方程和斯托克斯方程进行了分析。我们提出了一种简单、计算成本低、可靠且高效的几何简化误差后验估计方法。此外，我们还引入了一种考虑简化误差的几何细化策略：从完全简化后的几何模型出发，该算法在每个迭代步骤中确定需要添加到几何模型中以降低简化误差的特征。这些关键特征将在下一次迭代中被添加到（部分）简化的几何模型中，直至求解达到预设精度。最后，本文通过大量二维和三维数值实验对研究成果进行了验证说明。