# Shift operator for periodic functions

Dear all,

Assume u is a periodic scalar field on [0,1] (i.e. u(0)=u(1)) and the variational formulation of the problem depends on u(x) and u(x+a).

Is there a simple procedure to obtain u(x+a) from u(x) (right shift) in the same fespace ?

Thanks, Alexandru

Use periodic key word in fespace definition (see documentation or exemple)

Thank you ! I apologize, my question was not very clear : obviously, we need u in a periodic fespace of periodic functions but my question is how to use u and its shift u(x+a) (the shift of u) in the same variational formulation.

no way, I am sorry.But in this case u(x) == u(x+a) so no problem
And can you write what is the variational formulation in math.

Let me reformulate the question : let f be a periodic function of period 1, i.e. f(0)=f(1), declared as such in a FE space of periodic functions. Is there a way to use f(x+a) (the shift of f by a fixed amount but with 0<a<1, where obviously, x+a is understand mod 1) in a variational formulation (of a non-local problem) ?

No, because it is non local …