Thanks, Roy. For some of my earlier work I had used Kelly's error estimator for transonic flow problems, and it did exactly what you have described. It kept on refining the elements at the shock, and around the leading edge and trailing edge locations of an airfoil, which are locations of singularity. I am guessing that goal-oriented errors are better metrics to use, since for many applications it does not make sense to refine the shock locations beyond a certain point.
So, it likely makes more sense to use an L2 norm in these regions of shocks and singularities. Your comment about using patch recovery is due to not having a reference solution (on a very refined mesh), so post-processing the existing results is likely the only way to get a better reference solution. Do you think patch recovery is a good approach for shock locations? Would error norms based on H1-norm be better choices than those based on L2 norm for smoother solutions (no shocks, for example)? Thanks, Manav On Wed, Dec 4, 2013 at 3:51 PM, Roy Stogner <royst...@ices.utexas.edu>wrote: > > On Wed, 4 Dec 2013, Manav Bhatia wrote: > > My application is compressible Euler flow, so shock will appear in >> the computational domain. Is the L2 norm of density variable, compared >> with >> a reference solution (obtained on a very fine mesh), better or worse than >> an H1-seminorm on density? Should some other type of norm be considered? >> How about Kelly's error estimator? >> > > Trying to use an H1 norm (or anything derived from it, like Kelly) for > adaptive refinement on a shock problem can be a total *disaster*. > Basically your real H1 error is infinity, so any finite H1 error > estimates are likely to *increase* as you refine into the shock, and > this can lead to unstable refinement patterns where you just keep > refining in the spots you've already refined. I've got an example > slide or two somewhere I could hunt down and upload if you like. > > What worked decently for me was patch recovery in L2... this was just > part of an adjoint-weighted norm in my case, but I suspect it would > work fine for global error norm based refinement as well. Ben Kirk's > done a bunch of such studies; hopefully he'll chime in too. > --- > Roy > ------------------------------------------------------------------------------ Sponsored by Intel(R) XDK Develop, test and display web and hybrid apps with a single code base. Download it for free now! http://pubads.g.doubleclick.net/gampad/clk?id=111408631&iu=/4140/ostg.clktrk _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
