Dear Stephen,
At hanging nodes, there is definitely going to be a larger error due to
the approximation of the diagonal mass matrix. I do not remember the
exact details but to get a diagonal mass matrix you need to assume an
interpolation in addition to the approximation leading to the mass
lumping. If I remember correctly my co-worker Katharina Kormann
describes this in her paper:
https://doi.org/10.4208/cicp.101214.021015a
So in general, I would assume that a change of 1e-8 as you have in your
picture is simply the approximation error that occurs when going from
the initially interpolated solution to the new mesh. I would assume that
it goes away if you compute an "approximate" L2 projection where you
compute a right hand side (v, u_init) for test functions v and the
initial field u_init from ExactSolution of step-48 rather than
VectorTools::interpolate.
Have you tried that?
If the change is larger in other cases as you describe, I would be more
worried. Have you tried to investigate more? Does the projection instead
of interpolation help in that case, too?
The implementation should be correct as far as I can tell - we have
verified it on a large series of applications. In my experience, the
most tricky thing to get right regarding constraints and boundary
conditions is for nonlinear problems or implicit solvers with
inhomogeneous boundary data, but that appears to not be the case here...
Best,
Martin
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