From: John Peterson <jwpeterson@gm...>  20080826 15:39:24

On Tue, Aug 26, 2008 at 10:22 AM, Tim Kroeger <tim.kroeger@...> wrote: > Dear John, > > On Tue, 26 Aug 2008, John Peterson wrote: > >> On Tue, Aug 26, 2008 at 9:20 AM, Tim Kroeger >>> >>> 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. > > Oops, I'm very sorry. I mixed up quadrature points and nodes. What I meant > was that for a linear function on a tetrahedron, its maximal value can be > obtained by evaluating it at the corners of the tetrahedron only (and taking > the max of these values). Unfortunately the error is not a linear function in general, even though the approximate solution may be.  John 