From: John Peterson <jwpeterson@gm...>  20080826 14:40:54

On Tue, Aug 26, 2008 at 9:15 AM, Derek Gaston <friedmud@...> wrote: > In Encore at Sandia you get the choice to either compute L_Inf at the > quadrature points or at the nodes. > > There really isn't a good way to give L_Inf for a finite element > calculation.... because our solutions are continuous functions. The finite > difference guys would just take the difference at all the nodes and find the > largest one.... but that doesn't quite work for us (especially with higher > order elements). Given the exact solution and gradient, one could presumably come up with a little function optimization scheme which finds (a local) max on each element. The trouble would still be knowing whether the max found was actually the global max for that element... > Personally, I prefer finding the L_Inf error at quadrature points... one > nice thing about this is that if you want a better calculation of your > error... you just up your number of quadrature points. This is essentially > the same thing as comparing to a nonpolynomial exact solution (one you > can't integrate exactly).... you do _something_ that will give you a good > answer... but if you want a better answer you crank up the quadrature rule. Good point about increasing the number of quadrature points to get a better Linfty approximation. And as long as you are using a different quadrature rule for estimating the error than was used when computing the FE solution, I don't think the error can possibly be superconvergent at the quadrature points any more.  John 