Enquiry on problem definition

Dear all,

The weak formula of my problem is here:

(\nbala u, \nabla v) = (f, v * Xi) - (\nabla u0, \nabla (v * Xi)) ,

where u0, Xi is known. And u, v and u0 are in FEM space V1, while Xi is in FEM space V2 and V1 and V2 are difference in the mesh size. Then the code in FreeFEM is:

  solve P1(u,v)=

Now, I want to change the weak formula to this form:

(\nbala u, \nabla v) = (f, I_{h}(v * Xi)) - (\nabla u0, \nabla I_{h}(v * Xi)) ,

where I_{h} is the interpolation operator on FEM space V1.

Since v and Xi are in different FEM spaces, I do not know how to get the interpolation result and use it on the problem definition. Would you please tell me how to solve this? Thank you so much for your help!

Sincerely yours,