Problem
Research questions and friction points this paper is trying to address.
adaptive mesh refinement
marking strategies
finite element method
error estimation
computational efficiency
Marking strategies for adaptive mesh refinement: An efficiency-focused benchmark study for steady solid and fluid mechanics problems
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
adaptive mesh refinement
marking strategies
error estimation
statistical outlier detection
finite element method
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