I tried SolutionTransfer class, but because the DoFHandler is set in the 
constructor and assumed to be refined (or coarsen), we cannot use that 
solution to interpolate to a completely different mesh. Instead, a solution 
is to use VectorTools::interpolate_to_different_mesh() to a mesh that stays 
constant:

    Vector<double> interpolated_solution;

    interpolated_solution.reinit(dof_handler_export.n_dofs());

    VectorTools::interpolate_to_different_mesh(dof_handler, solution, 
dof_handler_export, interpolated_solution);


The result can be interpolated using vtkTemporalInterpolator. I uploaded the 
result at 60fps of step-26 here: https://www.youtube.com/watch?v=1jUUlwOA2fU


Cheers,

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