Different behaviour of error norms

ganesh

Dear Friends,

I am looking at the norms of error with refinement in a restricted region where the flow is smooth and devoid of discontinuities. The grid in the region is nearly uniform. I observe that the norms in L_\infty have a lower asymptotic slope compared to those in L_1. I know that the asymptotic rate is independent of the norm for a fixed dimension vector space, but refinement means the dimension of the error vector is increased, and the equivalence is lost. Could anyone give a specific example they have come across when this has happened for continuous flows ? (I have already seen LeVeque's notes where this can be illustrated for a discontinuity, and also seen it in my work with shocks).

Thanks in advance

Ganesh