The ideas behind the robust a posteriori error estimators can be applied to develop efficient adaptive mesh refinement strategies for singularly perturbed problems. By utilizing the error estimators derived from the Fortin operators, one can identify regions in the domain where the solution exhibits large errors or gradients, indicating the need for mesh refinement.
Adaptive mesh refinement strategies can be implemented based on these error estimators to selectively refine elements in regions of interest, such as boundary layers or areas with sharp gradients. This targeted refinement approach can help improve the accuracy of the numerical solution while minimizing computational costs associated with uniform refinement.
Additionally, the adaptive strategies can be coupled with error indicators that take into account the singular perturbation parameter and mesh size, allowing for a balanced refinement process that accounts for the specific characteristics of the problem. By iteratively refining the mesh based on the error estimators, one can achieve an optimal mesh configuration that efficiently captures the solution behavior in singularly perturbed problems.