SubsamplingVTKWriter seems broken

I have been using a regular VTKWriter to print the solutions of my PDE solver. When I discovered some artifacts in the VTK output (see the issue on PDELab), I set up a SubsamplingVTKWriter to further investigate. However, now I find new artifacts that are not related to grid refinement.

For our module, we set up a testing suite in which we compare the results (VTK files) of our PDE solver for a pseudo 1D case with the solution provided by an ODE solver. Regarding the residuals for both the solution (head) and its weighted gradient (flux), some structured wave-like patterns emerge for subsampling levels >0.

Here's a residual plot for subsampling levels 0, 1, and 2 on a static grid. y-axis shows the physical height, x-axis shows the residual.

This is the VTU file for subsampling level 2: ode_higherorder_0008-00029.vtu

This is a screenshot of the flux in a more complex transient case with subsampling:

Could this somehow be related to the issue I'm having with the visualization after local grid refinement?