## Re: [Libmesh-users] Comparison of solutions on different grids

 Re: [Libmesh-users] Comparison of solutions on different grids From: Tim Kroeger - 2008-08-26 15:36:44 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 under-predict the L-infty 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 1-point > quadrature rule. But this implies it's not true for a 2-point > 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). >> 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. Yes, I agree with that. Also, there is a different error in my patch: In parallel, I sum up the L-infty norms of all the processors, instead of taking their max value. I will send you a corrected patch tomorrow. Sorry again. Best Regards, Tim -- Dr. Tim Kroeger Phone +49-421-218-7710 tim.kroeger@..., tim.kroeger@... Fax +49-421-218-4236 MeVis Research GmbH, Universitaetsallee 29, 28359 Bremen, Germany Amtsgericht Bremen HRB 16222 Geschaeftsfuehrer: Prof. Dr. H.-O. Peitgen