oscillation patterns with time

During my Featool simulations,  I found oscillation patterns with time (e.g. for the concentration variable). My question is how to know if this oscillation is caused by a numerical issue? I expect that there will be a oscillation pattern in my case due to the mechanism inherent with it, but I found that this oscillation changed with the time step or discretization in featool. For my model simulations with fine discretization and fine time steps, it will take very very long time to test it.  

It is quite difficult to give a general answer as it is very problem/model specific. In general you would ideally try to get mesh and/or time step independent results (when your results stop changing when refining mesh and/or time steps). Depending on your physics model you can try to tune the artificial stabilization settings. Also with FEATool you can also use other solvers (currently FEniCS, OpenFOAM, SU2) for the same problem to verify that the results are correct.