Dear Niek,
This does indeed look strange. I cannot give an immediate answer
unfortunately. It looks like the problem appears in a single element
layer close to the boundary and does not seem to propagate into the
domain. Can you confirm this? Since I would expect a wrong Neumann
boundary condition to extend further into the domain (through the
diffusive term), I wonder whether you really look at a Neumann boundary
or whether it actually is a Dirichlet boundary. (If I remember
correctly, the problem setting in step-51 specified Dirichlet conditions
on that particular boundary.) In case of a Dirichlet boundary, my guess
is that you do not correctly take the time-dependent conditions into
account. Essentially, you would need to modify the constraint matrix
each time with data from project_boundary_conditions and make sure that
your solution vectors get the correct values set.
Best,
Martin
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