> The tool I work on here at work can compare any two arbitrary
> solutions to each other... even with completely non-nested grids.  The
> user gets to decide what kind of crime they want to commit though.
> Often (if the meshes are really dissimilar) we'll use an overkill
> rendezvous mesh to transfer both of the original solutions to first...
> then compare them on that grid. (Note: To do this in libMesh use two
> MeshFunctions and 3 meshes)
> 
> My favorite way though... is just to lay down a super fine quadrature
> rule and sample both grids at those quadrature points.  Sure... on one
> of the meshes you'll be integrating non-smooth functions with Gauss
> quadrature... but the results are usually pretty good.
> 
> I do think that some of the capabilities in this code at my current
> job are going to be put into libMesh over the next year.  libMesh
> already has a lot of the infrastructure for it... it wouldn't be too
> hard to make it a little more generic.


Take a look at src/apps/grid2grid.cc.  It is a little dated and tuned for a
specific code, but it is an 70% solution that could guide the
implementation.

This was implemented specifically for Bill to do mesh refinement studies as
part of his thesis.  Specifically, he wanted to demonstrate ||u - u_fine||
where the meshes spanned the same space and were not nested.

We essentially followed Derek's suggested approach...  We used an overkill
quadrature rule on the fine mesh.

-Ben


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