On Tue, Aug 26, 2008 at 10:27 AM, David Knezevic <[EMAIL PROTECTED]> wrote: > Hi all, > >>> What about returning this value as the DISCRETE_L_INF norm instead? In >>> particular since the FEMNormType enum offers this norm anyway. >> >> I think this might be confusing ... the DISCRETE_ versions are meant >> to be for R^n vectors, and in this case of course you can get the >> "exact" L_INF. I'd prefer adding a new enum called APPROXIMATE_L_INF >> (or something similar). The user would know immediately that he was >> getting an approximation to the true L-infty norm, and in the >> documentation we could mention (as Derek said) that one can improve >> the approximation by increasing the number of quadrature points. > > > But the L2, H1 etc errors in ExactSolution are computed using quadrature > rules, so they are just approximations as well. As a result, it seems to me > that the L_INF norm based on sampling at quadrature points is the natural > counterpart for the Sobolev norms currently available in ExactSolution.
Well... yeah but it still feels it's a different class of approximation deserving a different enum. Errors in computing the L2 and H1 errors are due to quadrature error, which can be bounded in terms of higher-order derivatives of the exact solution. The approximate L_INF norm calculation (as we have defined it here) may not have an error representation which is quite so well-defined ... then again maybe it does? Seems to me it would depend strongly on the number of sampling points as well. > Also, regarding the superconvergence issue, if we have superconvergence in > the L_INF norm at the quadrature points, and we use that quadrature rule to > compute the L2 error, then won't we just get the same superconvergence in > the quadrature-based L2 error as well? I think you are right, so in general one should always use a different quadrature rule, unless I am mistaken about that superconvergence property. For the life of me, I can't remember where I heard that and I'm starting to wonder if I may have made it up :-) -- John ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
