Convergence issue in nearest-projection mapping in fenics-fenics HT case for complex domain

A convergence study was conducted for the tutorial HT/partitioned-heat/fenics-fenics with nearest-projection and nearest-neighbor mappings for a simple interface (linear edge interface parallel to Y-axis) and a complex interface (Circular interface bounded in a rectangular domain). The simple interface study shows good results of improvement from nearest-neighbor to nearest-projection. The complex domain is visualised as follow:

The convergence study results are as follows:

It is seen that there is no significant improvement in the error plot when nearest-projection mapping is used instead of nearest-neighbor. One possible explanation is the error induced due to the RBF interpolation strategy being used contributes significantly to the total error and hence masks the effects of an improved mapping. Further investigation needs to be done.