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：对计算域进行局部修改通常是为了简化网格剖分过程并降低计算成本与内存需求。然而，移除域中的几何特征往往会在相关微分问题的求解中引入不可忽略的误差。本研究将文献[1]的结果推广至包含任意数量不同诺伊曼特征的域，并针对泊松方程、线弹性方程及斯托克斯方程展开分析。我们提出了一种简单、计算成本低、可靠且高效的几何去特征化误差后验估计器。此外，还引入了一种考虑去特征化误差的几何细化策略：从完全去特征化的几何体出发，该算法在每个迭代步骤中确定需添加至几何模型以降低去特征化误差的特征。这些重要特征将在下一步迭代中被加入（部分）去特征化的几何模型，直至解达到指定精度。最后通过一系列二维与三维数值实验对本文工作进行验证说明。