huyanzhou,

in the documentation , it's said in the case of mesh with moved vertices is
> refined a few step later, should do as follows:
> 1. save the offset applied to every vertex,
> 2. call communicate_locally_moved_vertices function
> 3. apply the opposite offset
> 4. call communicate_local refining or coarsening the meshly_moved_vertices
> function
> 5.  refining or coarsening the mesh
>
> i don't quite understand the 5 step.
> 1. what's the meaning of offset here? is it the move vector for every
> vectices in this step, or the whole move vector which will make the mesh
> return to original mesh?
>

The offset is the total move vector that will make the mesh return to its
original state. Only the mesh without any displacements has valid positions
for all the cells (including artificial ones).

2. we add the opposite offset , does this means we need apply the offset
> again after  refining or coarsening ?
>

Yes. The offset vector should be transferred to the new mesh via
SolutionTransfer. Then you can apply it again.

An alternative to moving the vertices is using MappingFEField or
MappingQEulerian.

Best,
Daniel

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