Adaptive mesh refinement (AMR) is indispensable for efficient finite element analyses. However, its performance depends not only on the refinement itself but also on strategy to mark elements for refinement and the way it is tuned. This work compares classical marking methods (maximum, Dörfler bulk-chasing, quantile) with non-classical, statistically based approaches (z-score, Isolation Forest), all driven by the residual-based Kelly error estimator and tested on steady solid and fluid mechanics problems. The study finds quantile and z-score markings to be the most robust, Dörfler effective for large bulk parameters, and maximum marking sensitive to irregular fields. Isolation Forest can rival top classical methods with a generous contamination level but may fail under aggressive settings. These results offer practical guidance for selecting marking strategies that balance refinement aggressiveness and computational cost in adaptive FEM workflows.

翻译：自适应网格细化（AMR）对于高效有限元分析至关重要。然而，其性能不仅取决于细化过程本身，还取决于标记待细化单元的策略及其调优方式。本研究比较了经典标记方法（最大值法、Dörfler体追赶法、分位数法）与非经典的统计学方法（z分数法、孤立森林法），所有方法均基于残差驱动的Kelly误差估计器，并在稳态固体与流体力学问题上进行测试。研究发现分位数与z分数标记最为稳健，Dörfler法在大体追赶参数下有效，而最大值标记对不规则场敏感。孤立森林法在宽松的污染水平设定下可与经典方法媲美，但在激进设定下可能失效。这些结果为自适应有限元工作流中平衡细化激进性与计算成本的标记策略选择提供了实用指导。