Marking strategies for adaptive mesh refinement: An efficiency-focused benchmark study for steady solid and fluid mechanics problems

TL;DR

This study compares classical and statistical marking strategies for adaptive mesh refinement in finite element analysis, providing guidance on their robustness and efficiency for steady solid and fluid mechanics problems.

Contribution

It introduces and evaluates non-classical, statistically based marking methods alongside classical ones, highlighting their relative robustness and effectiveness.

Findings

Quantile and z-score markings are most robust.

D"orfler marking is effective with large bulk parameters.

Isolation Forest can match classical methods with proper tuning.

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, D\"orfler 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, D\"orfler 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.