I am running a mesh independence study. I start with Mesh 1 and proceed up to Mesh 4, each time doubling the number cells in the mesh. In parallel, I am comparing my computational results to experimental data. M. 1 shows poor results. M. 2 shows a significant improvement and a good match to experimetnal results. M. 3 and M. 4 produce identical results, that are only slightly different from M. 2. It would then seem sensible to pick M. 3 as my final mesh. But it seems that the results are too smooth, loosing some of the fine details, produced by M. 2 (and observed in the experiments).
Can there actually be some sort of overcorrection? Could it be that the mesh independent solution is not necesarily the best one?