discret solution regularity
 

let P_h be the L2 orthogonal projector P_h : L2(0,1) ----> L2_h

L2_h is L2 discret

h is the step size

is this true

U in H1(0,1) <===> lim || Grad_h P_h U || ?

h-->0 L2_h

If we have a discret solution U_h, how can i get the regularity of the contnuous solution U from U_h ?

Thanks.