From: John Peterson <jwpeterson@gm...>  20080826 15:05:37

On Tue, Aug 26, 2008 at 9:20 AM, Tim Kroeger <tim.kroeger@...> wrote: > Dear John, > > On Tue, 26 Aug 2008, John Peterson wrote: > >> I'm not sure about your implementation of L_INF. You're taking >> >> e_{\infty} = max_q e(x_q) >> >> where x_q are the quadrature points. In fact, isn't the solution >> sometimes superconvergent at the quadrature points, and therefore this >> approximation could drastically underpredict the Linfty norm? > > Oh, I see, I (again) forgot that people are using different ansatz functions > than piecewise linear (for which this is obviously correct). Sorry, I'm a little slow. The formula above is correct for piecewise linears? I can see this for linear elements in 1D, with a 1point quadrature rule. But this implies it's not true for a 2point rule... etc. > 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.  John 