Adaptive Refinement in Advection–Diffusion Problems by Anomaly Detection: A Numerical Study
Round 1
Reviewer 1 Report
see the attached pdf file
Comments for author File: 
Comments.pdf
Author Response
We are grateful to the referee for his/her comments on the manuscript. The paper has been revised as suggested.
Author Response File: Author Response.pdf
Reviewer 2 Report
This is a fine a paper about a-posteriori error estimation for finite element simulation of the transport equation and subsequent mesh refinement. The contribution of the paper is to use automatic anomalous detection to select which elements should be refined.
Suggestions / minor comments
- Since Section 2.2 is the main contribution of the paper, an algorithmic box could help other researchers to implement it.
- In Fig. 3, the refinement about the right corners of the right mesh looks weird. Do the authors know the reason? This funny beaviour of the ZZ error estimator has been detected in other papers, too.
- In the caption of Fig. 3, for clearness I'd write "gradient recovery" instead of simply "gradient".
- In Tables 3, 10 , the last mesh with the largest number of nodes has more error that the previous mesh (with less nodes), specially in the H1 norm. Does this make sense?
- In Figs. 4, 7, 9, 11, 12, the numbers in the color legend cannot be read.
- About Fig. 14, indeed the final mesh of the Neumann method looks weird. For some reason, it seems the conclusion is that the residual error estimator works best. Note also that there exist specific residual-based error estimators for stabilized methods, that use the stabilization parameters within the error estimator.
Author Response
We are grateful to the referee for his/her comments on the manuscript. The paper has been revised as suggested.
Author Response File: Author Response.pdf
