On Wed, Apr 16, 2008 at 9:27 AM, Roy Stogner <[EMAIL PROTECTED]> wrote: > > On Wed, 16 Apr 2008, John Peterson wrote: > > > > Just out of curiosity, what would be the "right thing" to do in order > > to compare two meshes with different (still nested) refinement > > patterns or two solutions on completely non-nested grids? > > > > Loop over one grid. On each element, if the other grid is coarser, > you integrate here. If the other grid is finer, you get the > corresponding ancestor element there and integrate on all its active > descendants. That way you get the numerical integration right up to > floating point error, without worrying about quadrature error.
That should work great for the nested case. For the arbitrarily mismatched grids I think you must have to do something like Derek suggested and introduce a "transfer" Mesh which is somehow the "union" of both meshes you are comparing. In the nested case, differing p-levels would also be interesting. Should I then perform my integration over the mesh which has a single high-p element or over the one that chose to split it into multiple low-degree elements having small h? The answer probably depends on the smoothness of the true solution. > > > > It's not immediately obvious to me what such a comparison would > > actually tell you in any case... > > > > Oh, well I just meant that *what* to do to integrate between two such > grids was obvious; *why* to do such a comparison isn't obvious to me > either. If you're contrasting two different refinement strategies > then you generally want to compare them to a completely finer > reference solution, not to each other. > > I bet you'd usually still get a good error indicator for grid A in the > places where grid B was more refined, and vice versa; running into > pollution effects would be a nightmare, though. That's where my line of thought was heading. In problems with a singularity the simple "is h finer here or there?" test can fail due to non-local effects. -J ------------------------------------------------------------------------- This SF.net email is sponsored by the 2008 JavaOne(SM) Conference Don't miss this year's exciting event. There's still time to save $100. Use priority code J8TL2D2. http://ad.doubleclick.net/clk;198757673;13503038;p?http://java.sun.com/javaone _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
