From: John Peterson <jwpeterson@gm...>  20080826 15:54:25

On Tue, Aug 26, 2008 at 10:27 AM, David Knezevic <dave.knez@...> 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 Linfty 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 higherorder 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 welldefined ... 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 quadraturebased 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 