Dear all
A theory question:
The question I have is motivated by the adoption of Rothe's method in Step-23
of the example problems. There it states that if one were to use spatial
adaptivity between time steps then terms obtained from the previous time step
n-1 would need to be interpolated using interpolation functions based on the
mesh at t_{n-1}. Thus one has terms from different meshes at t_n and t_{n-1}
occurring in the weak form. Step-23 does not use spatial adaptivity but points
one to Step-28.
In Step-28 one needs to integrate solutions obtained on different meshes. The
different meshes are obtained for different energy groups. Thus, while they
derive from a common mesh, the meshes could be separated by various levels of
refinement. This is unlike Step 23 where the mesh is separated by only one
refinement / coarsening step between n and n-1.
If one were to adopt an adaptive strategy for Step 23 would it not suffice to
simply transfer the solution vector X at the end of step n-1 to the refined
mesh at the beginning of step n. Thus, you have X_{n-1} (the solution from the
old mesh) interpolated to the new mesh at t_n and you use the same
interpolation functions defined for the current time step?
Is this not essentially the methodology adopted in Step 33? There adaptivity is
used but no mention is made of constructing interpolation functions on
different meshes.
Many thanks
Andrew
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